My list is by no means exhaustive, they are just the books that I have encountered. The hardest part of making a video like this is trying to pronounce all the author's names correctly so my apologies in advance for any that I said wrong :P Also in Australia we tend to say 'maths' instead of 'math' and there is very little consistency in which I choose to use.
Tibees i have questions, do you like competition math or word problems? I love doing this although i get most of them wrong, but i like to see the solutions. This is because they are creative and cool to know for later problems.
Legendary Calculus books (Real analysis of 1 and n variables) in Eastern Europe is Mikhail Fihtengolc Kurs differencialnogo i integralnogo ischisleniya Tom 1, 2, 3 and the problem book "Anti-Demidovich (Lyashko I.I., i Dr.)."
"Calculus Made Easy" by Silvanus P. Thompson is one of the best calculus books. Reads like a novel and is over 100 years old and can be downloaded for free now, but its also still in print.
I agree 100%. I worked my way through that book very carefully, doing every problem. It may be the ONLY math book I've ever owned in which the author has a sense of humor. GREAT BOOK. (One of the commenters mentioned that it "lacked rigor." Well, what of it? As Thompson says (paraphrasing here), "You're right! But why should that matter? You don't need to know how a watch works in order to use it. Same is true of calculus. Learn to use it now. You can get the rigor later, if you need/want it.
@Harsh Raval Mathematical rigor and proper understanding are not the same. Mathematical rigor is often only needed to exclude the most pathological exceptions that would cause a theorem not being true. In the overwhelming number of cases this rigor, as necessary as it is, does not help in understanding at all, but hinders people to grasp the basic concepts apart from some pathologies. Mathematicians are the only scientists that arrogantly feel proud about being not understandable. In every other science people try to do their best to be understandable and embrace every means to do so, including visualization and simple examples. Bourbaki style abstract math is the biggest hindrance for the widespread use of math and I am sick of it.
It’s a great book and I’m a huge fan. When I went back to it years later I found his definition of integration was wrong. But not to take away from this - the rest was phenomenal and changed my life
Not boring in the least! I'm 48 years old and I have just started my studies in math. The things that I once found boring are now all I want to do. I am a self taught and well rounded drummer like Buddy Rich. Not quite as great as Buddy but as close as I could possibly get and am still striving to get there. Drums are all about patterns and once you master a particular pattern it opens up a wormhole to other galaxies of rhythms and syncopations and I will be forever be learning these patterns. It is the same for mathematics for me. Drums and math are two of the same and the list that you just introduced is going to open up a whole other Universe for me to absorb. Thank you for all the videos you post! You are a wealth of knowledge and you speak with such clarity so please keep posting videos and I will keep watching. Thank you!
The most important math books for a modern student are Velleman 'How to Prove It' and Bloch 'Proofs and Fundamentals'. Work these books out and you will never have serious issues with math. Bloch has also written 'The Real Numbers and Real Analysis' which is a perfect book on the foundations of real analysis, it's so perfect that I wanna cry.
Nick Sm I'm awful at maths, but really loved my formal logic class in philosophy. These sound more like what we were studying, though obviously with a different goal. I will look for these.
@@imPyramd, that's why I think these books are quite important. Real analysis is not really that hard if one knows basic stuff about logic and formal tools for working with sets and functions.
@@KhanKhan-tp4ch, you are talking nonsense. Why should books about proof techniques teach anybody geometry, trigonometry or topology in the first place?
My best math teacher was a mad crazy Englishman who taught me math at a high school in France. His name was Mr. Baugh and he taught us calculus, algebra, analytical geometry, trig and probability. He referred to us as the blockheads - pas douée pour le math . He always said he wanted students who had no mathematics but who were extraordinarily good at Latin (sic loquitur). He spoke in a manner that proved he was completely mad and one girl said it sounds like broken French with an English accent but I can't understand a word he says. Mr. Baugh inspired me to swot - hit the books - so I was totally prepared before the lessons as I knew his language was incomprehensible. It worked until we hit probability. In order to understand probability one needs good clear language so I did not do well in that aspect of math as his musings were gibberish to me. I was not alone, except for Gilbert who seemed to understand him. Later on in life I studied Latin and I understood why Mr. Baugh had loved its precision and exactness - "know the correct ending," After this high school college was a breeze and I shuffled through with middling grades and no effort. Later in life however, when faced with difficult choices and unsolvable problems I reached back across time to the insane muttering of that mad, crazy bastard who came to my aid down the years and in my mind I saw him put the numbers on the board and say " prove to me you lot are not hopeless." He is long dead. When he marched into heaven he read the sign put up by the students - " she was always the fastest of ships (said of a very clever girl in class).
Tibees you’re really an inspiration for any student, you just make the school seem, not easy, but worthy. I like your personality and I’m looking forward to be like you. Greetings from Mexico and keep it going 🇲🇽
I love "Measurement" by Paul Lockhart. It gives a great introduction to thinking about geometry and calculus by guiding you to great exercises without giving you the answers. It's like having a great teacher guiding you.
If you are looking for a single book to start with on math that covers the basics of the entire spectrum of subject in math, I can suggest "Mathematics For The Millions: How To Master The Magic Of Numbers" by Lancelot Hogben. It really helped me understand how each area of mathematics is related to solving problems in the real world and the writer assumes the reader has little or no background in the subject matter. First published in 1937, it is the older books and their authors that I believe had a talent for reaching students interested in complex subjects like Math.
Hogben is a readable book, I read this book and after it "Einführung in die Matrizenrechnung" (matrix algebra) before I studied electrical engineering/technical informatics.
I agree about munkre's topology, havent read the other book tho. But analysis on manifolds is in my opinion the best book that deals with multivariable calculus a little bit more seriously and is at the same time understandable for undergrads. Also Linear algebra done right by Axler is really great
This is a great list. The best resource i've seen for understanding linear algebra is the video series The Essence of Linear Algebra by 3blue1brown. Absolutely amazing, intuitive way to get the concepts, rather than just rote-learn. So good.
Agreed. Grant has a way of explaining topics that are difficult for those new to the topic or just struggling to understand it. His video series Essence of Calculus really helped me out. :-) Grant is a gift, no question.
What I love about 3blue1brown videos is that, let us put it the nerdish way, the subset of videos that are not shallow is nonempty and some of the insights contained there are nontrivial.
So do people think there's a lot of value in books rather than such videos for someone relearning maths? For me, I can't even sit down to do problems unless I have a complete comprehension of the underlying concepts. Like for calculus I've been watching a bunch of different explanations, the last thing I want to do is just 'x^2 -> 2x'. So books, more useful than videos for concepts?
Top intro stuff (IMhO): 1. Ian Stewart "Concepts of modern mathematics" - issued in 1980, now a bit forgotten. 2. Courant/Robbins "What is mathematics" - absolute classics. 3. "Infinitely large napkin" - google it. 4. "Concrete mathematics" by Knuth & gang - more toward discrete math.
I read part of "Infinitely Large Napkin" (written by a student) but I think the "Cambridge Notes" (written by a student) are sometimes more understandable/complete but also very compact.
I recently drove across the country, and stopped by every used bookstore that I saw in order to check the mathematics section. I really enjoy taking a look at the way that different books expose mathematics differently, and I'm also always looking to expand my collection. Based upon this, as well as my experience as a math major, I have several comments on what books should be used to learn mathematics. The key point is this: the right book to use is highly dependent upon what you want to learn, what parts of it you want to learn, and what interests you. Several of the books that are mentioned in the video are what I would call "applied textbooks", which will give good methods for solving individual problems, or classes of techniques for applying mathematical tools to real world problems. "elementary linear algebra" and "early transcendentals" would fall into this category. These have almost nothing in common with some of the books here, like "principles of mathematical analysis", Dummit and Foote, or, to some degree, spivak's "calculus", which I would call "pure mathematics texts". These texts are based upon developing mathematical techniques through proving things. Most of so-called "pure math" is based around making mathematical statements and proving them. Spivak's calculus covers similar material to "early transcendentals", but each topic that is introduced will be rigorously defined (to some degree) and proved. The latter will teach you how to find the integral of e^2x, while the former will teach you how to show that taking that integral is possible, and examine the properties of integration (e.g. how do I know that the antiderivative of a continuous function is continuous, let alone differentiable). "principles of mathematical analysis" goes beyond this, wherein the backbone of the book is theorems, and its main goal is developing techniques for proving other things. Dummit and Foote probably wouldn't look very much like mathematics to the high-school reader, because it presumes that the reader is already very well versed in mathematical arguments. However, there is a third group of books, which aren't talked about all that frequently. These apply rigorous mathematical techniques to applied fields. Most of these books become accessible once someone has a background in linear algebra and multivariate calculus. For example, many books on optimization are fairly proof-based, however they have tangible examples that help to keep the exposition grounded. The book that convinced me to be a math major wasn't an abstract algebra textbook, it wasn't number theory, or non-euclidean geometry. The book is called "optimization in function spaces" by Amol Sasane, and it is accessible to anyone with a good grasp of linear algebra and abstract vector spaces, and multivariate calculus. Finite element analysis textbooks (a common method of dealing with PDEs in engineering) often have these properties as well, but a thorough understanding of these books requires a good understanding of differential equations first. Game theory, mathematical biology, and many other fields have books like these, which delicately introduce a new reader to the idea of rigorous proof without scaring them half to death. What I have discovered is that I really do love rigorous proof, I just find most of mathematics endlessly dry until I find something to apply it to. For me, the third category of books is perfect. For some people (like my roommate), the math is enough in and of itself, so the second "pure math" category is for them. Others will never catch the "rigorous proof" bug, and that's fine. There will always be books in the first category, and the math you'll learn from them will be tremendously useful in whatever field has driven you to learn math.
Eli Maor wrote several books. My first exposure to him was Trigonometric Delights. A masterpiece with an enticing title. I purchased several copies and sent one to my brothers daughter who was taking Trig at the time. e: The Story of a Number, and June 8, 2004--Venus in Transit are both excellent. In looking on Amazon I see he hasn't been idle, so I now have a few more to read.
I'm currently a junior high school student that has exhausted all the high school maths curriculum that my school teaches so now I bought the book Mathematical methods for physics and engineering by Riley, Hobson, and Bence. The book was recommended to me by a great RUclipsr called Simon Clark. Absolutely love it, I've already bought it since and study maths with the book and with free online lectures. I'll soon start Calc 3 (multivariate calculus), then linear algebra and after that differential equations. Thank you very much +Tibees for inspiring me to study maths and physics. Love you!
Definitely NOT boring at all.... :-) Getting the right books (and teachers!) is critical IMO... ...In the past one was stuck with whatever was in the reading list, at the school/public/Uni library, on display at Technical Books et al., or if you were smart and not too shy (I was only half-qualified :'( ) to ask Librarians or bookstore people for suggestions or publishers' catalogues... so pretty much Pot Luck (especially in smallish-town New Zealand). Having someone like you (and collecting opinion from your viewers) list some good ones could save people lots of grief and time. Thanks for doing this one! :-)
Your videos are very nutritive for advanced students in high schools or students in first year of mathematics and surely they have changed the live of many of them. I congratulate you. I wanted to attach my list because I think that for mathematicians and physicists your list is necessary but not enough: 1.- Elementary Classical Analysis by J. Marsden or Mathematical Analysis by L. Kudriavstev or Calculus by D. Zill. 4:43 2.- Linear Algebra by S. Friedberg A. Insel L. Spence or Linear Algebra by V. Voevodin or Foundations of Linear algebra by A. Maltsev or Linear Algebra by S. Lang. 5:36 3.- Ordinary Differential Equations by V. Arnold or Differential Equations with Applications and Historical Notes by G. Simmons. 6:51 4.- Introductory Complex Analysis by R. Silverman or The Theory of Analytical Functions: A brief course by A. Markushevich. I would like to add that T. Needham has covered of glory!! 7:40 5.- Introductory Real Analysis by A. Kolmogorov and S. Fomin or Mathematical Analysis by T. Apostol or Hilbert Spaces with Applications by L. Debnath and P. Mikusinski. 8:54 6.- Abstract Algebra by I. Herstein or Introduction to Algebra by A. Kostrikin. 9:21 7.- Reason in Revolt by Ted Grant and A. Woods. 9:32 Your work about science diffusion will be rewarded by many students of science in the future because your work is love, and, as López Obrador says “The love is paid with love”.
I know I’m late to the party, but I wanted to thank you for this awesome books list. Started _Fermat’s last theorem_ yesterday and it’s very good. Hope I’ll find inspiration for digging more in depth in the fascinating world of maths! Again, thank you.
I would like to thank you but not for the content of the video this time but for your, I don't know, "energy" in it. You look positive, smily, nice, honest. It is simply contagious looking you giving the recommendation book. Thank you!
An amazing introduction textbook for calculus is "Introductory Mathematical Analysis" by Haeussler, Paul & Wood. I did not enjoy Math at all until I started studying from this book but its comprehensive explanations made me understand all the topics and I started enjoying it after a while. Definitely would recommend!
I think walter rudin is quite advance and will tough job to understand for beginners. So for basics, I usually gone through are as follows 1.Calculus Vol 1 and Vol 2 by J.H. Heinbockel 2. Calculus Early Transcendentals 3. Calculus by Gilbert Strang.
The two texts that got me through my engineering degree and are keepers for me are... Erwin Kreyszig's Advanced Engineering Mathematics, and... Howard Anton's Calculus. Other keepers are Engineering Thermodynamics by William Reynolds and Henry Perkins (my professor :-) ), and for psych Henry Gleitman's Psychology.
I love books! And I have some books that change my mind. Some books: A Problem Book in Complex Analysis - Daniel Alpay, Topology - Munkres, How to Think Like a Mathematician, Linear Algebra - Hoffman and Kunze, Linear Algebra - Prasolov, Linear Algebra Done Right - Sheldon Axler, Proofs from THE BOOK - Agner Ziegler, Love and Math - Edward Frenkel, Course of Analysis - Elon Lages Lima (Brazilian Book about analysis), Real Mathematical Analysis - Pugh, Collection of Barry Simon A comprehensive course of Analysis and, finally, Naive Set Theory - Halmos.
This is a great list.But personally I would suggest people to try out Mathematical methods in Physics by Boas. It is written in a way that mathematics seems too easy. Particularly for people interested more in Physics than Maths.
I had a terrible teacher for Algebra 1 in ninth grade. My mom hired a tutor that school year for me. I took Algebra 2 in tenth grade because it was required. You explain things very well and are a great teacher.
Thank you for the lovely video! As an old physics major myself (emphasis on the word 'old'), may I make a couple of other recommendations? For another person's look back at his life as a mathematician (in addition to the famous book by Hardy you mentioned), I highly recommend "Adventures of a Mathematician," by Stanislaw Ulam. Born in Poland but later an emigrant to the United States, Ulam does an incredible job recalling the flavor of intellectual life in the old European capitals during the period between the two world wars. I especially like the scenes, which are particularly well drawn, of mathematicians sitting in cafes for hours talking and doing mathematics. If there was ever a romantic period (and place!) of mathematics, this was it. Ulam became a very close and lifelong friend of John von Neumann and many other of the 20th century's most famous mathematicians and physicists; he was also involved in the work at Los Alamos for the Manhattan Project. He had an incredible sense of humor - something not typically associated with the stereotypical mathematician. Just one example, from his widow (who clearly shared a good sense of humor), who added a postscript to the book in a later edition published after Ulam's death: "He [Ulam] used to say 'the best way to die is of a sudden heart attack or to be shot by a jealous husband.' He had the good fortune of succumbing to the first, though I believe he might have preferred the second.' (Ulam's widow, Francoise Ulam) My second recommendation is "Infinity' by Lillian Lieber. (Giving you a 2nd woman for your list!). Lieber was the head of the mathematics department of Long Island University in New York (U.S.) back in the 1930s I believe. She wrote a series of books on mathematics for the layman that are not at all dumbed down. They are actually quite sophisticated, but presented in an easygoing and entertaining manner. I first ran across them when I was in high school in the 1970s and was amazed. "Infinity" carefully goes through Cantor's discovery of transfinite numbers. It's an amazing book. She also wrote a book called "The Einstein Theory of Relativity" where she discusses both the special and general theories. (She goes into detail on tensor calculus in developing the apparatus needed to properly explain the latter.) All of her "popular" math books are charmingly illustrated by her husband, Hugh Lieber, who I believe was head of the art department at the same university. Anyway, that's my two cents worth! I hope someone finds these recommendations useful. Cheers!
Most of what people are proposing is great for those with a sound foundation. The problem is that 99.95% of the population does not have that sound foundation.
As a maths graduate I have a few suggestions: - fun book: "Physics of star trek by Lawrence Krauss - advanced book if you really want to stretch yourself: Astronomical Algorithms by Jan Meeus. Meeus was a famous mathematician of astronomy; in this book he derives the formulae for an eclipse, when the moon is furthest away etc. Basically he does an exhaustive and stunning discussion of any classical astronomy formula. A brilliant book. If you have ever wondered how do they work out where those planets are he gives you the answers. - historical book - Longitude by Dava Sobel. Your list is pretty good. Anton and Linear algebra. That was a fun book!
Abbott's Understanding Analysis is a very nice alternative to Rudin's. It is also probably a better book than Rudin for self learning, or for desperate students (it worked for me).
Rudin is better!! More rigorous and a better prep. for grad level analysis. Abbott does not cover a lot of the integral topics like Darboux integral or Riemann - Stil integral. There is even no topology in R^n or a thing about measures.
Thank you for the information you have provided here and the extra references stimulated in the comments. I loved to see and hear you talk about mathematics books. I was not bored at any time listening to you! 🙂
Some more fun books: _Fantasia Mathematica_ and _The Mathematical Magpie_ are collections of mostly literary pieces (short stories and poems) on mathematical topics, including the story "The Devil and Simon Flagg", in which a man offers to sell his soul to the devil if the devil can prove Fermat's Last Theorem by a deadline (this was written long before Wiles). _Sphereland_ is an expansion on the ideas in _Flatland._ _Stress Analysis of a Strapless Evening Gown_ is a collection of humorous mathematical pieces, including a proof that Alexander the Great's horse did not exist, and had an infinite number of legs. Of course, everyone should be aware of the many collections of Martin Gardner's "Mathematical Games" columns. I'll also mention Hofstadter's _Gödel, Escher, Bach._ Lastly, don't forget Lewis Carroll. In addition to the two Alice books, which anyone interested in math or physics must read (especially Gardner's _Annotated Alice_ ), he also did some books of puzzles, which are still available.
So glad Mary Boas is on your list. I just sent it (yesterday) to my grandson in Australia. My dad had it on his bookshelf and when he died my cousin’s husband asked to have it. (He worked at GCHQ!) That was thirty years ago. So I found a second hand copy for my grandson who loves maths. He is 16 in May, so it’s in his birthday parcel. RUclips is so clever!
If you like comic books with serious subjects, you should try reading some Manga Guides. They are great as introductionary courses for young adults or to brush up forgotten knowledge. Eg Manga Guide to Statistics, Manga Guide to Microprocessors, etc...
I recommend for pure math classes: 1. Linear algebra- hoffman 2. Mathematical analysis- Apostol 3. Elements od real Analysis- Battle 4. Mathematical Analysis vol 1 &2 - Zorich 5. Abstract Algebra- Dummit foote 6. Topology- Munkers 7. Functional analysis- Rudin 8. Advanced Calculus- buck 9. The Princeton lectures by stein & shakarchi 10. Second course in mathematical analysis- burkill 11. Advanced Algebra- roman 12. course in group theory- Humphreys 13. Theory of Ordinary Differential Equations- coddington 14. A First Course in Algebraic Topology- Czes Kosniowski Among others
I study bioengineering and when I was on 3rd semester I took multivariable calculus as an optional subject (everybody in bioengineering is afraid of taking it despite the fact that multivariable calculus is fundamental to understand nature), reading Calculus by James Stewart was the best thing I could do, the book was so clear and explains very well the idea of parcial derivatives and multiple integrals that I felt in love with it. In the other hand, Differential Equations by Dennis Zill is a good book that covers multiple ways to solve an ordinary differential equation (e.g. Laplace transform). I found Introducción al Algebra Lineal by Howard Anton in a sort of recycle paper can, I think someone threw it away and I took it, the book was basically new, but the book I use for algebra is Elementary Linear Algebra by Grossman. By the way, I think that talking about math books is very interesting because I always want to know which book is the best about explaining complicated math ideas.
The best way to understand nature is to LOOK at it. I've got a gut feeling that it's not THAT complicated as we make it out to be. For example, a drop of water forms a sphere and it doesn't need pi. Just a hunch.
Hi, what does a bioengineer do? My two great passions are math and life, but it seems like math is not very much used.in biology, so i dont know if to study biology or mathematics Im a high school senior btw
pene asteca I wanted to study biology too, but I couldn’t. As Bill Nye once said in an interview: “engineers use science to make things and solve problems”. In this case, bioengineers solve problems related with biology and medicine (which is applied biology). I have no regrets for studying bioengineering because we should learn about every different science, for example, you need to understand math (from algebra to differential equations), chemistry (from reactions to the math and physics behind those reactions), physics (from classical mechanics to electricity and magnetism) and, of course, biology (from cells to the human body and all the physics, chemistry and math behind the processes that occur in the body and cells). A bioengineer could work improving processes or products using living organisms (biotechnology) or elaborating devices such an electrocardiogram (ECG), electroencephalogram (EEG), etc., those devices allow doctors to measure physiological parameters and make decisions based no those measures. In summary, bioengineering mixes math and biology very well jajajaja. Good luck with your decision.
It's also interesting to go into completely different aspects of math. Calculus can diverge into many different areas for many different subjects. For a bioengineer, I would imagine that you could make use of stochastic modeling or stochastic calculus. Biology is very big on statistical analysis too and I feel that statistical mechanics and the study of entropy in the physics of life would help your broader view of the universe. Life is a sort of negative entropy that is moving towards more complexity and intelligence as "time" goes on. The formation of life itself came from pockets of low temperature spontaneous environments.
@@CandidDate Except our senses aren't capable of handling many phenomena as according to our evolution, specifically, in the context of biology, phenomena that are very small, very numerous and very un-uniform. Though you may attempt to observe a single particle with kinetic energy and its displacement with respect to some origin within an isolated system as a function of time, this becomes much more complex when there is a system of particles, all or varying kinetic energies. And, furthermore, the system may not be isolated, and, in fact, the walls may even be elastic in the sense that kinetic energy would be lost from the system with every particle that collides with the wall of the system. Perhaps, energy may even enter that system accordingly as thermal energy. Not only does what was supposed above call for the use of tensor analysis, but differential equations as well, differential equations that aren't necessarily ordinary or linear. And with a strong ability to predict complex biological systems with mathematical certainty, don't be surprised with the rewards that would be reaped, that we could not only optimize medicine to an incredible degree, but could even engineer our bodies with great confidence and make ourselves more intelligent, healthier and even more attractive. You're not the sharpest tool in the box, but you stated: _"The best way to understand nature is to LOOK at it."_ With such confidence that you even typed "look" in all caps. You remind me of a horrific mathematics teacher I have currently. When stupid people become supremely arrogant, it just makes life difficult for everyone else.
Visual Complex Analysis is a wonderful book that really opened my eyes on the topic. Before reading it I thought complex numbers had no real meaning and were just arbitrary filler. Prime Obsession is another wonderful book and does a really clear explanation of the Riemann Hypothesis and the breakdown of the various areas of mathematical study in general.
I recommend "Euler's Gem: The Polyhedron Formula and the Birth of Topology" to anyone about to take algebraic topology for the first time. It puts it in a historical context. The Greeks began classifying the polyhedra and mathematicians over the centuries extended that idea and extended that idea and arrived at homology and homotopy which math grad students study today and is an area of active research.
Hi Tibees! I really wanna recommend the book "Math, Better Explained" by Kalid Azad because, although by no means a college level textbook, it acts like an introductory guide to some very basic math concepts, and explores those concepts in fun and intuitive ways which makes for some convenient quick learning. Btw I really admire and like your content!
From a more pure maths angle, An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is excellent, and it is something you can come at with only a highschool level grasp of mathematical proof, and work through to the more advanced subjects. For inequalities of the sort used in Analysis, the Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele is an excellent problem based book for developing knowledge and intuition. From an applied maths angle, Advanced Engineering Mathematics by Erwin Kreyszig contains introductory information on just about any sort of mathematics one comes across in applications, and is a good companion to most undergraduate applied maths courses. I still make use of it, many years after having graduated. My all time favourite linear algebra textbook is A Guide to Advanced Linear Algebra by Steven H Wientraub. It doesn't contain problems, but it is what I use as my go to linear algebra textbook for basic theoretical results, because there are clear and elegant proofs of everything any mathematician would need to know about linear algebra in any context one is likely to come across in an undergraduate course. It makes a good companion to a regular linear algebra text that covers first and second year material in a more problem oriented manner.
I am a Maths teacher, I think 80-90% of the population will find Maths rather difficult or boring. For children in the western countries, they need to find this subject interesting or fun for them to learn whereas in the east the children are or less compelled to learn like I do. In the end, I learnt something and I much appreciated it even though I learnt it the hard way. More importantly being competent in Maths contribute to me being what I am and help me to think in a more logical manner or clear thinking which most young people I am afraid lack. Good on you to produce this video.
THOMAS CALCULUS -EARLY TRANSCENDENTALS BY George B. Thomas, Jr. In my opinion this book is best and good approach to learn calculus in fine way. Very useful for engineers.
A recommendation for a good leisure-type math book that is really easy to read is "Alex's adventures in numberland" by Alex Bellos, it explains various mathematical concepts like logarithms, higher dimensions, how they arrived at pi, euler's number and how they discovered them. Really good read :)
Kwantimus Prime Yes!! Thanks for the recommendation! I really enjoyed Alex Bellos’ book because of the various mathematical proofs like the Pythagorean theorem and such. Thanks again for the recommendation.
Love the videos! Keep on making them! Grew up in the following sequence: Counting, Grouping, Addition, Subtraction, Multiplication, Division, Powers, Basic Roots, Algebra I + Geometry, Algebra II + Trig, Pre-Calc, Calc I, Calc II, Calc III, Diff Eq, Linear Algebra + Logic, Prob & Stat + Combinatorics, Graph Theory + Analysis, ...
I recently purchased a used calculus textbook, both to bone up my my skill set and to support a small local used bookstore. In the prologue was written, "Keep in mind that every single problem in this text has already been solved by somebody, so your ability to solve those problems gives you nothing unique." I like their frankness.
I sometimes see this recommended but I think it's unnecessarily technical and heavy for an introduction to those topics. Most people would probably fare better with lighter material.
needhams book is great! Also, I'm reading "Higher Arithmetic" by H.Davenport. It's a number theory book recommended by Andrew Wiles. It's rather short at ~200 pages but dense.
on social media there are two types of girls : 1. who are shaking their flesh online and promoting vulgarity and nudity. 2. the girls like you , highly educated and hardworking, promoting knowledge and helping to creating a better world. hatts off to you ma'am..................
Good recommendation re Simon Singh - He's amazing :-) I have his Cryptography and Simpson's Maths books, not yet the Fermat's Last Theorem one (it's defo on my list though :-) ). BTW have you seen what he did to reform UK libel law? - He called out Chiropractic as mostly bunk, paid heavily for it - but won out in the end. Huge respect from me! :-)
Sarah Greenwood It's such a dense read. I had a class which used the textbook, and the instructor was not very good. I had to take notes on the textbook as my only notes, and it was quite difficult. I had to do research online to understand some things the author didn't spend much time on, too.
Visual Complex Analysis from Needham is one of the most beautiful math books that I ever seen!! I really love the way in how he introduce the concepts using geometry and Mobius transformations 😺
It's late night in Buenos Aires right now to think in maths but I wanted to mention these books. I lovehate them A First Course in Calculus by Serge Lang Calculus by Michael Spivak Vector Calculus by Jerrold E. Marsden&Anthony Tromba Notas de Algebra by Enzo Gentile Linear Algebra by Kunze&Hoffman Complex Variables and Applications by Churchill&Brown Probability & Statistics by Seymour Lipschutz An Introduction to Wavelet Analysis by David Walnut Statistical and Computational Methods in Data Analysis by Siegmund Brandt Love your channel
Francisco Russo no te olvides de "probabilidad y estadistica para ciencias e ingenieria. Walpole" "calculus vol 1 y 2. Apostol" "ecuaciones diferenciales. Denis Zill" 😉
10:24 not for passionate people like everyone else here liking and commenting this video. The more we read the more we crave ! You convinced me, I subscribe ! Greetings from Canada !
Hi. I recommend "Proofs and Fundamentals" by Ethan Bloch, its lecture is very clear and "eye-opening" for a first semester student. And for Linear Algebra, Gilbert Strang's MIT OCW lectures are excellent, so I bet its book on the subject is worth reading.
for a historical perspective I recommend ' Men of Mathematics ' by E T Bell and ; Mathematics and it's History ' by John Stillwell who is associated with the University at Melbourne .
Linear Algebra - Hoffman and Kunze, Steven Roman (actually Roman has several pretty solid books on everything from mathematical finance to writing excel macros). Differential Geometry - Lee Topology - Munkres -> Hatcher Algebra - Herstein (or how to teach someone algebra by brutally punishing them) Analysis - There are no good analysis books. I work in an analysis field. I have yet to find a non-trash book. Bass is terrible too but at least it's free and concise. One day an analyst will figure out that you're allowed to draw pictures and it will be amazing.
I solved both volumes of Apostol's Calculus (25-30 per cent of exercises in almost 4 years), and now I'm solving Apostol's Analysis and Differential Equations by George Simmons. I want to achieve a real understandying of certain areas of Maths, studying the correct sequences of contents, without blank spaces. Your election and methods depends on you want to reach. Maybe I could select better books, but I feel confortable with the results I have obtained.
The best "book" for a particular course is often a copy of the notes taken by a student in the previous year. If the topics of the course are unchanged then you can fill in gaps in the notes without having to take down all the equations and steps and concentrate better on the lecturer. Not all lecturers hand out printed notes. Even fewer make these available the week before - either handed out or online. Some courses go a step further and have material produced by more than one person - the lecture given by one, the handouts drafted by another and an online version of the lecture given by a third. This certainly worked well for the early stages of a degree course.
Yeah! Calculus by Micheal Spivak is what I used back in 1975-76 during my first year in college at the university of Havana Cuba. Other books I used mostly in Cuba were: Mathematical Analysis by Tom M. Apostol, and Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus by Micheal Spivak too. I wish I could remember more books since I do remember to spent one semester, a real semester or about 5 months, learning topics about geometry with an introduction to lineal algebra, and then I took at least 2 or 3 semesters of pure lineal algebra and group theory, but I do not remember the books I used. By the way, I was never able to complete my BA in Cuba, but I did finish it here; however, I can tell that I learned more Math in all my 5 semesters in Cuba than my last 4 short semesters of college, semesters which were no more than 4 months, to obtain my BA in Math.
Brian Tristam Williams What is so wrong about complementing someone's appearance? He didn't do it in a creepy or perverse fashion, and he also addressed the topic of the video, I think his comment was uncommonly polite to be honest. You're just being touchy
Brian Tristam Williams ruclips.net/video/6AF9QrTJD4U/видео.html >Great vid, but audio is really soft and coming out the left channel only Oh wow, the vid is so "great" you had to comment on its sound. Disgusting.
Recommended readings for the graduate students: John Bell - Speakable and Unspeakable in Quantum Mechanics Roger Penrose - The Road to Reality Kurt Gödel - On Formally Undecidable Propositions of Pincipia Mathematica and Related Systems Saul Kripke - Naming and Necessity
Mathematics is a discovery like finding a new bug or seeing fireworks for the first time. I have fought classical teaching methods and strongly despair letting any incomplete paper or grade below maximum. I threw out the books at a academy I was teaching at. The previous teachers gave the students no hope and told them they had no future in their interest. I felt as an engineer that there is a way to experience math and to challenge the students. I did find a British man’s perspective in MAX PETERS College algebra, A Barrons study guide. I took 8 through 12-year students with his book since the extreme incremental progress and the concise inclusion of everything through to pre-calculus was impressive and exciting. It was not me so much but being a leader and teacher with a great tool, it was possible to get the high school level to get API in their college entrance exam. For me I could feel correlation of things and fit. It has always been my desire to understand history around mathematics. Einstein wanted to find common relative something in a war-torn world. There seemed no solution but in mathematics and physics there was a window to give hope that there was something that we all had in common down to the smallest things to the largest. That is what drove him, I think. Moving around , different languages and Religious division. Sometimes people think they need special environment or circumstances to be creative. History shows that in extreme circumstances and great pain was the most accomplished and the most pressure to find answers. A small boy on a ted talk stated something profound. Stop learning and start thinking and creating. Let the process teach you. At some point and often this is what is needed periodically if not constantly for some. Go to the garden and build a dirt city with friends the creativity and problem solving will amaze you. The Prussian school system is defective as is grades. Testing abilities and watching what is done with provided tools and materials is a start. OOps too much. But my passion is in it. I worked on the premise and in reality for all students to complete all exercises and to get 100% until they get to the next levels. Some methods as Saxon method forced students to re hash and get a mix of previous problem sets to keep in in mind. This was depressing for me and the students can be forced. But math is progression and experience to see a future . Exercises to go out and measure a building or tree with a stick and a shadow, impress students that life is mathematical not the other way around. Your presentations are attractive and personable. I think teaching in conversational and demonstration method is the way to go. I would think a game could be created to demand solving math and physics to progress. I mean extensively.
@@MeatCatCheesyBlaster That still doesn't explain why someone would feel intimidated. When I meet someone more knowledgeable or skillful than myself, I usually feel curious and look upon it as an opportunity to ask questions and learn something. If that person is jerk or just wants to put me down, well...that's their problem. Usually that sort of person is just hiding behind a fancy title. In reality they're not really as skillful as the title suggests; hence they put others down to discourage them from asking questions and uncovering the fact that they are really just a phony.
Howard Anton's textbook on "Calculus" is excellent...35 years ago when I was a freshman in engineering school and now when I need to brush up. It is for a solid three-semester course, with plenty of special topics.
(1) Mathematical Methods for Physics and Engineering: A Comprehensive Guide by K. F. Riley and M. P. Hobson (Cambridge University). This book is for Physicists and Engineers at undergraduate level. I believe the 3rd Edition is the latest. This book even has intro to Group Theory and Representation Theory! There is also a Students Solution Manual for 'Mathematical Methods for Physics and Engineering: A Comprehensive Guide'. Also try the following books by Geoff Stephenson (Imperial College, London): (2) Mathematical Methods for Science Students by G. Stephenson. (3) Advanced Mathematical Methods for Engineering and Science Students by G. Stephenson and P.M. Radmore. (4) An Introduction to Matrices, Sets and Groups for Science Students by G. Stephenson. (5) Partial Differential Equations for Scientists and Engineers by G. Stephenson. (6) Special Relativity for Physicists by G. Stephenson and C.W. Kilmister. These G. Stephenson books were based on the mathematics courses he gave to Engineering and Physics undergraduates at Imperial College over the years.
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My list is by no means exhaustive, they are just the books that I have encountered. The hardest part of making a video like this is trying to pronounce all the author's names correctly so my apologies in advance for any that I said wrong :P Also in Australia we tend to say 'maths' instead of 'math' and there is very little consistency in which I choose to use.
Thanks for this information I think it will be very useful for my undergraduate engineering.keep helping us like this😃
But these things don't matter if you are learning science or maths , there are 224 countries probably all pronounce differently
Tibees i have questions, do you like competition math or word problems? I love doing this although i get most of them wrong, but i like to see the solutions. This is because they are creative and cool to know for later problems.
Legendary Calculus books (Real analysis of 1 and n variables) in Eastern Europe is Mikhail Fihtengolc Kurs differencialnogo i integralnogo ischisleniya Tom 1, 2, 3 and the problem book "Anti-Demidovich (Lyashko I.I., i Dr.)."
Paul Driver umm.. i am fine if you are like that just learn to keep it to yourself sometimes. It is incredibly off topic. To each its own
When I wanted to learn English and practise for my listening exam I was listening to her videos!
Me too following the same sprint :)
Misma historia para mí
Me too, greetings from Argentina
Wonderful
So did I, greetings from Colombia xd
"Calculus Made Easy" by Silvanus P. Thompson is one of the best calculus books. Reads like a novel and is over 100 years old and can be downloaded for free now, but its also still in print.
actually you're right it's still in print but out of copyright.
I agree 100%. I worked my way through that book very carefully, doing every problem. It may be the ONLY math book I've ever owned in which the author has a sense of humor. GREAT BOOK. (One of the commenters mentioned that it "lacked rigor." Well, what of it? As Thompson says (paraphrasing here), "You're right! But why should that matter? You don't need to know how a watch works in order to use it. Same is true of calculus. Learn to use it now. You can get the rigor later, if you need/want it.
Harsh Raval what books are good for understanding concepts and why they work? Any example preferably around pre cal and intermediate algebra.
@Harsh Raval Mathematical rigor and proper understanding are not the same. Mathematical rigor is often only needed to exclude the most pathological exceptions that would cause a theorem not being true. In the overwhelming number of cases this rigor, as necessary as it is, does not help in understanding at all, but hinders people to grasp the basic concepts apart from some pathologies. Mathematicians are the only scientists that arrogantly feel proud about being not understandable. In every other science people try to do their best to be understandable and embrace every means to do so, including visualization and simple examples. Bourbaki style abstract math is the biggest hindrance for the widespread use of math and I am sick of it.
It’s a great book and I’m a huge fan. When I went back to it years later I found his definition of integration was wrong. But not to take away from this - the rest was phenomenal and changed my life
Not boring in the least! I'm 48 years old and I have just started my studies in math. The things that I once found boring are now all I want to do. I am a self taught and well rounded drummer like Buddy Rich. Not quite as great as Buddy but as close as I could possibly get and am still striving to get there. Drums are all about patterns and once you master a particular pattern it opens up a wormhole to other galaxies of rhythms and syncopations and I will be forever be learning these patterns. It is the same for mathematics for me. Drums and math are two of the same and the list that you just introduced is going to open up a whole other Universe for me to absorb. Thank you for all the videos you post! You are a wealth of knowledge and you speak with such clarity so please keep posting videos and I will keep watching. Thank you!
I which you the best!
Drumchef hubdad I’m with you brother: I’m 41 and beginning my math journey as well.
I am sure you will do great.
i admire your resilience and perseverance
Well done
The most important math books for a modern student are Velleman 'How to Prove It' and Bloch 'Proofs and Fundamentals'. Work these books out and you will never have serious issues with math. Bloch has also written 'The Real Numbers and Real Analysis' which is a perfect book on the foundations of real analysis, it's so perfect that I wanna cry.
Nick Sm I'm awful at maths, but really loved my formal logic class in philosophy. These sound more like what we were studying, though obviously with a different goal. I will look for these.
Nick Sm real analysis makes me cry. I might check those books out
@@imPyramd, that's why I think these books are quite important. Real analysis is not really that hard if one knows basic stuff about logic and formal tools for working with sets and functions.
@@KhanKhan-tp4ch, you are talking nonsense. Why should books about proof techniques teach anybody geometry, trigonometry or topology in the first place?
you say it's so perfect im curiouuuus. im social student that wanna learn math
My best math teacher was a mad crazy Englishman who taught me math at a high school in France. His name was Mr. Baugh and he taught us calculus, algebra, analytical geometry, trig and probability. He referred to us as the blockheads - pas douée pour le math . He always said he wanted students who had no mathematics but who were extraordinarily good at Latin (sic loquitur). He spoke in a manner that proved he was completely mad and one girl said it sounds like broken French with an English accent but I can't understand a word he says. Mr. Baugh inspired me to swot - hit the books - so I was totally prepared before the lessons as I knew his language was incomprehensible. It worked until we hit probability. In order to understand probability one needs good clear language so I did not do well in that aspect of math as his musings were gibberish to me. I was not alone, except for Gilbert who seemed to understand him. Later on in life I studied Latin and I understood why Mr. Baugh had loved its precision and exactness - "know the correct ending," After this high school college was a breeze and I shuffled through with middling grades and no effort. Later in life however, when faced with difficult choices and unsolvable problems I reached back across time to the insane muttering of that mad, crazy bastard who came to my aid down the years and in my mind I saw him put the numbers on the board and say " prove to me you lot are not hopeless." He is long dead. When he marched into heaven he read the sign put up by the students - " she was always the fastest of ships (said of a very clever girl in class).
what a nice story
The key to any good maths textbook is to have a picture on its cover completely unrelated to the subject it's discussing.
Why?
@@arigato9340 He's joking
just your voice calms me down and your videos reduce my stress. Thanks Tibees!
Tibees you’re really an inspiration for any student, you just make the school seem, not easy, but worthy. I like your personality and I’m looking forward to be like you. Greetings from Mexico and keep it going 🇲🇽
I love "Measurement" by Paul Lockhart. It gives a great introduction to thinking about geometry and calculus by guiding you to great exercises without giving you the answers. It's like having a great teacher guiding you.
If you are looking for a single book to start with on math that covers the basics of the entire spectrum of subject in math, I can suggest "Mathematics For The Millions: How To Master The Magic Of Numbers" by Lancelot Hogben. It really helped me understand how each area of mathematics is related to solving problems in the real world and the writer assumes the reader has little or no background in the subject matter. First published in 1937, it is the older books and their authors that I believe had a talent for reaching students interested in complex subjects like Math.
It has a chapter on how logarithms were discovered that I thought was pretty good. (My high school math teacher could not explain that to us.)
Thanks for suggesting this book
Hogben is a readable book, I read this book and after it "Einführung in die Matrizenrechnung" (matrix algebra) before I studied electrical engineering/technical informatics.
Thank you so much, I finished _Fermat’s last theorem_ today. It was a very good entertaining math book, I really enjoyed it.
"Introduction to Manifolds" By Loring Tu is super accessible and absolute GOLD, same with Munkre's "Topology"
I agree about munkre's topology, havent read the other book tho. But analysis on manifolds is in my opinion the best book that deals with multivariable calculus a little bit more seriously and is at the same time understandable for undergrads. Also Linear algebra done right by Axler is really great
Talking about math is never boring, thank you for sharing your experience with us
This is a great list.
The best resource i've seen for understanding linear algebra is the video series The Essence of Linear Algebra by 3blue1brown. Absolutely amazing, intuitive way to get the concepts, rather than just rote-learn. So good.
Agreed. Grant has a way of explaining topics that are difficult for those new to the topic or just struggling to understand it. His video series Essence of Calculus really helped me out. :-) Grant is a gift, no question.
Yeah! That LA playlist completely changed the way I look at mathematics. Grant is awesome.
What I love about 3blue1brown videos is that, let us put it the nerdish way, the subset of videos that are not shallow is nonempty and some of the insights contained there are nontrivial.
Hii kon
So do people think there's a lot of value in books rather than such videos for someone relearning maths? For me, I can't even sit down to do problems unless I have a complete comprehension of the underlying concepts. Like for calculus I've been watching a bunch of different explanations, the last thing I want to do is just 'x^2 -> 2x'. So books, more useful than videos for concepts?
"Math Major's Drug Deal"
I just wanna take a moment to appreciate that combination of words 😂
Ditto. I was rinsing with mouthwash when I heard her say it, and my computer nearly got some.
1st... You talk so calm and low, yet I'm so captivated when I listen to you.
2nd?
3rd?
4th?
Top intro stuff (IMhO):
1. Ian Stewart "Concepts of modern mathematics" - issued in 1980, now a bit forgotten.
2. Courant/Robbins "What is mathematics" - absolute classics.
3. "Infinitely large napkin" - google it.
4. "Concrete mathematics" by Knuth & gang - more toward discrete math.
I read part of "Infinitely Large Napkin" (written by a student) but I think the "Cambridge Notes" (written by a student) are sometimes more understandable/complete but also very compact.
I recently drove across the country, and stopped by every used bookstore that I saw in order to check the mathematics section. I really enjoy taking a look at the way that different books expose mathematics differently, and I'm also always looking to expand my collection.
Based upon this, as well as my experience as a math major, I have several comments on what books should be used to learn mathematics. The key point is this: the right book to use is highly dependent upon what you want to learn, what parts of it you want to learn, and what interests you.
Several of the books that are mentioned in the video are what I would call "applied textbooks", which will give good methods for solving individual problems, or classes of techniques for applying mathematical tools to real world problems. "elementary linear algebra" and "early transcendentals" would fall into this category. These have almost nothing in common with some of the books here, like "principles of mathematical analysis", Dummit and Foote, or, to some degree, spivak's "calculus", which I would call "pure mathematics texts". These texts are based upon developing mathematical techniques through proving things. Most of so-called "pure math" is based around making mathematical statements and proving them. Spivak's calculus covers similar material to "early transcendentals", but each topic that is introduced will be rigorously defined (to some degree) and proved. The latter will teach you how to find the integral of e^2x, while the former will teach you how to show that taking that integral is possible, and examine the properties of integration (e.g. how do I know that the antiderivative of a continuous function is continuous, let alone differentiable). "principles of mathematical analysis" goes beyond this, wherein the backbone of the book is theorems, and its main goal is developing techniques for proving other things. Dummit and Foote probably wouldn't look very much like mathematics to the high-school reader, because it presumes that the reader is already very well versed in mathematical arguments.
However, there is a third group of books, which aren't talked about all that frequently. These apply rigorous mathematical techniques to applied fields. Most of these books become accessible once someone has a background in linear algebra and multivariate calculus. For example, many books on optimization are fairly proof-based, however they have tangible examples that help to keep the exposition grounded. The book that convinced me to be a math major wasn't an abstract algebra textbook, it wasn't number theory, or non-euclidean geometry. The book is called "optimization in function spaces" by Amol Sasane, and it is accessible to anyone with a good grasp of linear algebra and abstract vector spaces, and multivariate calculus. Finite element analysis textbooks (a common method of dealing with PDEs in engineering) often have these properties as well, but a thorough understanding of these books requires a good understanding of differential equations first. Game theory, mathematical biology, and many other fields have books like these, which delicately introduce a new reader to the idea of rigorous proof without scaring them half to death.
What I have discovered is that I really do love rigorous proof, I just find most of mathematics endlessly dry until I find something to apply it to. For me, the third category of books is perfect. For some people (like my roommate), the math is enough in and of itself, so the second "pure math" category is for them. Others will never catch the "rigorous proof" bug, and that's fine. There will always be books in the first category, and the math you'll learn from them will be tremendously useful in whatever field has driven you to learn math.
Thanks for this insight
I knew i would find something of value in the comments. Really appreciate you giving a summarized 'summary' of the types of books she recommended.
You are really hardworking and dedicated
Respect
Thank you for the macro-conceptual input on the fields of mathematical erudition.
Bit of a random point, but I love the way your videos start IMMEDIATELY, without intro or other nonsense.
There are 30 thorns in that cactus
M T underrated comment
36 Thorns
39 plz
no, 36
Your comment is even more weird than the double slit experiment !
Nice job, Tibees. One of my favorite books is "e: The Story of a Number". I read it in 2008 and loved it. Will read it again.
Eli Maor wrote several books. My first exposure to him was Trigonometric Delights. A masterpiece with an enticing title. I purchased several copies and
sent one to my brothers daughter who was taking Trig at the time.
e: The Story of a Number, and June 8, 2004--Venus in Transit are both excellent.
In looking on Amazon I see he hasn't been idle, so I now have a few more to read.
I'm currently a junior high school student that has exhausted all the high school maths curriculum that my school teaches so now I bought the book Mathematical methods for physics and engineering by Riley, Hobson, and Bence. The book was recommended to me by a great RUclipsr called Simon Clark. Absolutely love it, I've already bought it since and study maths with the book and with free online lectures. I'll soon start Calc 3 (multivariate calculus), then linear algebra and after that differential equations. Thank you very much +Tibees for inspiring me to study maths and physics. Love you!
Work and think hard Dominik! There is a Fields Medal out there and you should win it by 30 with ten yrs to spare!
Definitely NOT boring at all....
:-)
Getting the right books (and teachers!) is critical IMO...
...In the past one was stuck with whatever was in the reading list, at the school/public/Uni library, on display at Technical Books et al., or if you were smart and not too shy (I was only half-qualified :'( ) to ask Librarians or bookstore people for suggestions or publishers' catalogues... so pretty much Pot Luck (especially in smallish-town New Zealand).
Having someone like you (and collecting opinion from your viewers) list some good ones could save people lots of grief and time.
Thanks for doing this one!
:-)
Your videos are very nutritive for advanced students in high schools or students in first year of mathematics and surely they have changed the live of many of them. I congratulate you.
I wanted to attach my list because I think that for mathematicians and physicists your list is necessary but not enough:
1.- Elementary Classical Analysis by J. Marsden or Mathematical Analysis by L. Kudriavstev or Calculus by D. Zill. 4:43
2.- Linear Algebra by S. Friedberg A. Insel L. Spence or Linear Algebra by V. Voevodin or Foundations of Linear algebra by A. Maltsev or Linear Algebra by S. Lang. 5:36
3.- Ordinary Differential Equations by V. Arnold or Differential Equations with Applications and Historical Notes by G. Simmons. 6:51
4.- Introductory Complex Analysis by R. Silverman or The Theory of Analytical Functions: A brief course by A. Markushevich. I would like to add that T. Needham has covered of glory!! 7:40
5.- Introductory Real Analysis by A. Kolmogorov and S. Fomin or Mathematical Analysis by T. Apostol or Hilbert Spaces with Applications by L. Debnath and P. Mikusinski. 8:54
6.- Abstract Algebra by I. Herstein or Introduction to Algebra by A. Kostrikin. 9:21
7.- Reason in Revolt by Ted Grant and A. Woods. 9:32
Your work about science diffusion will be rewarded by many students of science in the future because your work is love, and, as López Obrador says “The love is paid with love”.
Thanks for your list
Give me some LOVE/MATH!!!!
Lopez Obrador who doesn't understand basic economics? Lmao
(Or basic math involved in economics)
Super random encontrar gente hablando de Lopez Obrador en videos de matemáticos del otro lado del mundo
I know I’m late to the party, but I wanted to thank you for this awesome books list.
Started _Fermat’s last theorem_ yesterday and it’s very good. Hope I’ll find inspiration for digging more in depth in the fascinating world of maths!
Again, thank you.
The absolute boss book I found for Math learning was KA Stroud-Engineering Mathematics. I still use it today when I need a refresher.
I would like to thank you but not for the content of the video this time but for your, I don't know, "energy" in it. You look positive, smily, nice, honest. It is simply contagious looking you giving the recommendation book. Thank you!
An amazing introduction textbook for calculus is "Introductory Mathematical Analysis" by Haeussler, Paul & Wood. I did not enjoy Math at all until I started studying from this book but its comprehensive explanations made me understand all the topics and I started enjoying it after a while. Definitely would recommend!
I'm so happy that you mentioned Needham's Visual Complex Analysis :)
i got lost in her eyes. any books on how to get out
Haha so true.
Multidimensional Quantam Physics.
.m. me too. Gorgeous
Oh god kill me now plz
David Brumby ya
She is so pretty
I think walter rudin is quite advance and will tough job to understand for beginners. So for basics, I usually gone through are as follows
1.Calculus Vol 1 and Vol 2 by J.H. Heinbockel
2. Calculus Early Transcendentals
3. Calculus by Gilbert Strang.
The two texts that got me through my engineering degree and are keepers for me are... Erwin Kreyszig's Advanced Engineering Mathematics, and... Howard Anton's Calculus.
Other keepers are Engineering Thermodynamics by William Reynolds and Henry Perkins (my professor :-) ), and for psych Henry Gleitman's Psychology.
I love books! And I have some books that change my mind. Some books: A Problem Book in Complex Analysis - Daniel Alpay, Topology - Munkres, How to Think Like a Mathematician, Linear Algebra - Hoffman and Kunze, Linear Algebra - Prasolov, Linear Algebra Done Right - Sheldon Axler, Proofs from THE BOOK - Agner Ziegler, Love and Math - Edward Frenkel, Course of Analysis - Elon Lages Lima (Brazilian Book about analysis), Real Mathematical Analysis - Pugh, Collection of Barry Simon A comprehensive course of Analysis and, finally, Naive Set Theory - Halmos.
This is a great list.But personally I would suggest people to try out Mathematical methods in Physics by Boas. It is written in a way that mathematics seems too easy. Particularly for people interested more in Physics than Maths.
Orszag and Bender wrote the book on that subject long ago. Believed to be the best technical book ever written.
After having tons of calculus classes, I read George Boole's (Yes, that Boole) book on Finite Differences. I found it absolutely delightful.
She is good human from our planet to help those who seek to ease mathematics learning, Thank you.
Terence Tao is soooo brilliant. Looking forward to reading his book. Of course it's been a while I've passed Analysis I but... true love never fades!
I had a terrible teacher for Algebra 1 in ninth grade. My mom hired a tutor that school year for me. I took Algebra 2 in tenth grade because it was required. You explain things very well and are a great teacher.
Thank you for the lovely video! As an old physics major myself (emphasis on the word 'old'), may I make a couple of other recommendations? For another person's look back at his life as a mathematician (in addition to the famous book by Hardy you mentioned), I highly recommend "Adventures of a Mathematician," by Stanislaw Ulam.
Born in Poland but later an emigrant to the United States, Ulam does an incredible job recalling the flavor of intellectual life in the old European capitals during the period between the two world wars. I especially like the scenes, which are particularly well drawn, of mathematicians sitting in cafes for hours talking and doing mathematics. If there was ever a romantic period (and place!) of mathematics, this was it. Ulam became a very close and lifelong friend of John von Neumann and many other of the 20th century's most famous mathematicians and physicists; he was also involved in the work at Los Alamos for the Manhattan Project. He had an incredible sense of humor - something not typically associated with the stereotypical mathematician. Just one example, from his widow (who clearly shared a good sense of humor), who added a postscript to the book in a later edition published after Ulam's death: "He [Ulam] used to say 'the best way to die is of a sudden heart attack or to be shot by a jealous husband.' He had the good fortune of succumbing to the first, though I believe he might have preferred the second.' (Ulam's widow, Francoise Ulam)
My second recommendation is "Infinity' by Lillian Lieber. (Giving you a 2nd woman for your list!). Lieber was the head of the mathematics department of Long Island University in New York (U.S.) back in the 1930s I believe. She wrote a series of books on mathematics for the layman that are not at all dumbed down. They are actually quite sophisticated, but presented in an easygoing and entertaining manner. I first ran across them when I was in high school in the 1970s and was amazed. "Infinity" carefully goes through Cantor's discovery of transfinite numbers. It's an amazing book. She also wrote a book called "The Einstein Theory of Relativity" where she discusses both the special and general theories. (She goes into detail on tensor calculus in developing the apparatus needed to properly explain the latter.) All of her "popular" math books are charmingly illustrated by her husband, Hugh Lieber, who I believe was head of the art department at the same university.
Anyway, that's my two cents worth! I hope someone finds these recommendations useful. Cheers!
Most of what people are proposing is great for those with a sound foundation. The problem is that 99.95% of the population does not have that sound foundation.
As a maths graduate I have a few suggestions:
- fun book: "Physics of star trek by Lawrence Krauss
- advanced book if you really want to stretch yourself: Astronomical Algorithms by Jan Meeus. Meeus was a famous mathematician of astronomy; in this book he derives the formulae for an eclipse, when the moon is furthest away etc. Basically he does an exhaustive and stunning discussion of any classical astronomy formula. A brilliant book. If you have ever wondered how do they work out where those planets are he gives you the answers.
- historical book - Longitude by Dava Sobel.
Your list is pretty good. Anton and Linear algebra. That was a fun book!
Abbott's Understanding Analysis is a very nice alternative to Rudin's. It is also probably a better book than Rudin for self learning, or for desperate students (it worked for me).
Yes ,I think it is the best
Rudin is better!! More rigorous and a better prep. for grad level analysis. Abbott does not cover a lot of the integral topics like Darboux integral or Riemann - Stil integral. There is even no topology in R^n or a thing about measures.
But Rudin isn’t meant for a first year course to learn analysis. So no mate.
Thank you for the information you have provided here and the extra references stimulated in the comments. I loved to see and hear you talk about mathematics books. I was not bored at any time listening to you! 🙂
Some more fun books:
_Fantasia Mathematica_ and _The Mathematical Magpie_ are collections of mostly literary pieces (short stories and poems) on mathematical topics, including the story "The Devil and Simon Flagg", in which a man offers to sell his soul to the devil if the devil can prove Fermat's Last Theorem by a deadline (this was written long before Wiles).
_Sphereland_ is an expansion on the ideas in _Flatland._
_Stress Analysis of a Strapless Evening Gown_ is a collection of humorous mathematical pieces, including a proof that Alexander the Great's horse did not exist, and had an infinite number of legs.
Of course, everyone should be aware of the many collections of Martin Gardner's "Mathematical Games" columns.
I'll also mention Hofstadter's _Gödel, Escher, Bach._
Lastly, don't forget Lewis Carroll. In addition to the two Alice books, which anyone interested in math or physics must read (especially Gardner's _Annotated Alice_ ), he also did some books of puzzles, which are still available.
awesome, I need to check out some of these!
Cool thx.
Jesus loves you. Repent. Believe in the Gospel. It’s not about religion but about a relationship.
So glad Mary Boas is on your list. I just sent it (yesterday) to my grandson in Australia. My dad had it on his bookshelf and when he died my cousin’s husband asked to have it. (He worked at GCHQ!) That was thirty years ago. So I found a second hand copy for my grandson who loves maths. He is 16 in May, so it’s in his birthday parcel. RUclips is so clever!
you've got my like because of spivaks calculus :)
(also for fun check out logicomix and uncle petros and the goldbach conjecture)
If you like comic books with serious subjects, you should try reading some Manga Guides.
They are great as introductionary courses for young adults or to brush up forgotten knowledge.
Eg Manga Guide to Statistics, Manga Guide to Microprocessors, etc...
@@gonzothegreat1317 oh,i'll check them up.thanks!
I recommend for pure math classes:
1. Linear algebra- hoffman
2. Mathematical analysis- Apostol
3. Elements od real Analysis- Battle
4. Mathematical Analysis vol 1 &2 - Zorich
5. Abstract Algebra- Dummit foote
6. Topology- Munkers
7. Functional analysis- Rudin
8. Advanced Calculus- buck
9. The Princeton lectures by stein & shakarchi
10. Second course in mathematical analysis- burkill
11. Advanced Algebra- roman
12. course in group theory- Humphreys
13. Theory of Ordinary Differential Equations- coddington
14. A First Course in Algebraic Topology- Czes Kosniowski
Among others
I study bioengineering and when I was on 3rd semester I took multivariable calculus as an optional subject (everybody in bioengineering is afraid of taking it despite the fact that multivariable calculus is fundamental to understand nature), reading Calculus by James Stewart was the best thing I could do, the book was so clear and explains very well the idea of parcial derivatives and multiple integrals that I felt in love with it. In the other hand, Differential Equations by Dennis Zill is a good book that covers multiple ways to solve an ordinary differential equation (e.g. Laplace transform). I found Introducción al Algebra Lineal by Howard Anton in a sort of recycle paper can, I think someone threw it away and I took it, the book was basically new, but the book I use for algebra is Elementary Linear Algebra by Grossman. By the way, I think that talking about math books is very interesting because I always want to know which book is the best about explaining complicated math ideas.
The best way to understand nature is to LOOK at it. I've got a gut feeling that it's not THAT complicated as we make it out to be. For example, a drop of water forms a sphere and it doesn't need pi. Just a hunch.
Hi, what does a bioengineer do? My two great passions are math and life, but it seems like math is not very much used.in biology, so i dont know if to study biology or mathematics
Im a high school senior btw
pene asteca I wanted to study biology too, but I couldn’t. As Bill Nye once said in an interview: “engineers use science to make things and solve problems”. In this case, bioengineers solve problems related with biology and medicine (which is applied biology). I have no regrets for studying bioengineering because we should learn about every different science, for example, you need to understand math (from algebra to differential equations), chemistry (from reactions to the math and physics behind those reactions), physics (from classical mechanics to electricity and magnetism) and, of course, biology (from cells to the human body and all the physics, chemistry and math behind the processes that occur in the body and cells). A bioengineer could work improving processes or products using living organisms (biotechnology) or elaborating devices such an electrocardiogram (ECG), electroencephalogram (EEG), etc., those devices allow doctors to measure physiological parameters and make decisions based no those measures. In summary, bioengineering mixes math and biology very well jajajaja. Good luck with your decision.
It's also interesting to go into completely different aspects of math. Calculus can diverge into many different areas for many different subjects. For a bioengineer, I would imagine that you could make use of stochastic modeling or stochastic calculus. Biology is very big on statistical analysis too and I feel that statistical mechanics and the study of entropy in the physics of life would help your broader view of the universe. Life is a sort of negative entropy that is moving towards more complexity and intelligence as "time" goes on. The formation of life itself came from pockets of low temperature spontaneous environments.
@@CandidDate
Except our senses aren't capable of handling many phenomena as according to our evolution, specifically, in the context of biology, phenomena that are very small, very numerous and very un-uniform.
Though you may attempt to observe a single particle with kinetic energy and its displacement with respect to some origin within an isolated system as a function of time, this becomes much more complex when there is a system of particles, all or varying kinetic energies. And, furthermore, the system may not be isolated, and, in fact, the walls may even be elastic in the sense that kinetic energy would be lost from the system with every particle that collides with the wall of the system. Perhaps, energy may even enter that system accordingly as thermal energy.
Not only does what was supposed above call for the use of tensor analysis, but differential equations as well, differential equations that aren't necessarily ordinary or linear.
And with a strong ability to predict complex biological systems with mathematical certainty, don't be surprised with the rewards that would be reaped, that we could not only optimize medicine to an incredible degree, but could even engineer our bodies with great confidence and make ourselves more intelligent, healthier and even more attractive.
You're not the sharpest tool in the box, but you stated: _"The best way to understand nature is to LOOK at it."_
With such confidence that you even typed "look" in all caps. You remind me of a horrific mathematics teacher I have currently. When stupid people become supremely arrogant, it just makes life difficult for everyone else.
I dont need mathematics to see how wonderful You are. Thank You for spreading knowledge.
Visual Complex Analysis is a wonderful book that really opened my eyes on the topic. Before reading it I thought complex numbers had no real meaning and were just arbitrary filler. Prime Obsession is another wonderful book and does a really clear explanation of the Riemann Hypothesis and the breakdown of the various areas of mathematical study in general.
I recommend "Euler's Gem: The Polyhedron Formula and the Birth of Topology" to anyone about to take algebraic topology for the first time. It puts it in a historical context. The Greeks began classifying the polyhedra and mathematicians over the centuries extended that idea and extended that idea and arrived at homology and homotopy which math grad students study today and is an area of active research.
Hi Tibees! I really wanna recommend the book "Math, Better Explained" by Kalid Azad because, although by no means a college level textbook, it acts like an introductory guide to some very basic math concepts, and explores those concepts in fun and intuitive ways which makes for some convenient quick learning.
Btw I really admire and like your content!
Thanks for sharing!
From a more pure maths angle, An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is excellent, and it is something you can come at with only a highschool level grasp of mathematical proof, and work through to the more advanced subjects. For inequalities of the sort used in Analysis, the Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele is an excellent problem based book for developing knowledge and intuition. From an applied maths angle, Advanced Engineering Mathematics by Erwin Kreyszig contains introductory information on just about any sort of mathematics one comes across in applications, and is a good companion to most undergraduate applied maths courses. I still make use of it, many years after having graduated. My all time favourite linear algebra textbook is A Guide to Advanced Linear Algebra by Steven H Wientraub. It doesn't contain problems, but it is what I use as my go to linear algebra textbook for basic theoretical results, because there are clear and elegant proofs of everything any mathematician would need to know about linear algebra in any context one is likely to come across in an undergraduate course. It makes a good companion to a regular linear algebra text that covers first and second year material in a more problem oriented manner.
For linear algebra I also recommend “Linear Algebra Done Right” by Sheldon Axler, for me is the best linear algebra book ever
Willy Bilky I did’t know that book 😱, thanks for sharing!
Can anyone recommende me any calculus for higher mathematics book
Sorry for poor English
@@neerajbhatt700 I recommend you Calculus from Spivak,
@@ferolimen is this book for higher mathematics Buddy ?
I am a Maths teacher, I think 80-90% of the population will find Maths rather difficult or boring. For children in the western countries, they need to find this subject interesting or fun for them to learn whereas in the east the children are or less compelled to learn like I do. In the end, I learnt something and I much appreciated it even though I learnt it the hard way.
More importantly being competent in Maths contribute to me being what I am and help me to think in a more logical manner or clear thinking which most young people I am afraid lack.
Good on you to produce this video.
Oh I look fondly on that Stewart book, we used the 7th edition back at my university. Genuinely fun times.
THOMAS CALCULUS -EARLY TRANSCENDENTALS BY George B. Thomas, Jr.
In my opinion this book is best and good approach to learn calculus in fine way. Very useful for engineers.
A recommendation for a good leisure-type math book that is really easy to read is "Alex's adventures in numberland" by Alex Bellos, it explains various mathematical concepts like logarithms, higher dimensions, how they arrived at pi, euler's number and how they discovered them.
Really good read :)
Elliot Alderson 'The Moment of Proof' by Donald C. Benson is also a good read. It goes into mathematical discoveries and proofs.
Kwantimus Prime Yes!! Thanks for the recommendation! I really enjoyed Alex Bellos’ book because of the various mathematical proofs like the Pythagorean theorem and such.
Thanks again for the recommendation.
@@funkahontas sonsgood😊
Love the videos! Keep on making them!
Grew up in the following sequence: Counting, Grouping, Addition, Subtraction, Multiplication, Division, Powers, Basic Roots, Algebra I + Geometry, Algebra II + Trig, Pre-Calc, Calc I, Calc II, Calc III, Diff Eq, Linear Algebra + Logic, Prob & Stat + Combinatorics, Graph Theory + Analysis, ...
Why not logic before Linear Algerbra?
and here comes me who only studies from notes.
I recently purchased a used calculus textbook, both to bone up my my skill set and to support a small local used bookstore. In the prologue was written, "Keep in mind that every single problem in this text has already been solved by somebody, so your ability to solve those problems gives you nothing unique."
I like their frankness.
What about "In a mind for Numbers" ? It teaches how to be good at math and science..
I thought that book was more about how to learn than learning math itself (I haven’t read it yet, that’s what I got from reviews)
it's a great book to learn how to learn
Thanks for including Elementary Linear Algebra - Howard Anton
This is very great
Might I add Stein & Shakarchi's four-part analysis series?
I sometimes see this recommended but I think it's unnecessarily technical and heavy for an introduction to those topics. Most people would probably fare better with lighter material.
Thanks for showing a direction in mathematics
needhams book is great! Also, I'm reading "Higher Arithmetic" by H.Davenport. It's a number theory book recommended by Andrew Wiles. It's rather short at ~200 pages but dense.
on social media there are two types of girls : 1. who are shaking their flesh online and promoting vulgarity and nudity.
2. the girls like you , highly educated and hardworking, promoting knowledge and helping to creating a better world.
hatts off to you ma'am..................
Good recommendation re Simon Singh - He's amazing :-)
I have his Cryptography and Simpson's Maths books, not yet the Fermat's Last Theorem one (it's defo on my list though :-) ).
BTW have you seen what he did to reform UK libel law? - He called out Chiropractic as mostly bunk, paid heavily for it - but won out in the end. Huge respect from me!
:-)
I am very weak in maths and really can't understand anything, but I like listening to you.
Mathematical methods for physics and engineering is good for anyone doing maths as well.
Sarah Greenwood It's such a dense read. I had a class which used the textbook, and the instructor was not very good. I had to take notes on the textbook as my only notes, and it was quite difficult. I had to do research online to understand some things the author didn't spend much time on, too.
It is a big book
You’ve grown to be one of my favorite youtubers.
Currently working through Boas at UC Berkeley!
Gael Flores Great book. Will give you the foundations to study physics. (y)
Visual Complex Analysis from Needham is one of the most beautiful math books that I ever seen!! I really love the way in how he introduce the concepts using geometry and Mobius transformations 😺
It's late night in Buenos Aires right now to think in maths but I wanted to mention these books. I lovehate them
A First Course in Calculus by Serge Lang
Calculus by Michael Spivak
Vector Calculus by Jerrold E. Marsden&Anthony Tromba
Notas de Algebra by Enzo Gentile
Linear Algebra by Kunze&Hoffman
Complex Variables and Applications by Churchill&Brown
Probability & Statistics by Seymour Lipschutz
An Introduction to Wavelet Analysis by David Walnut
Statistical and Computational Methods in Data Analysis by Siegmund Brandt
Love your channel
Saludos desde Capital. Que bueno es ver a alguien argentino viendo este canal también. Definitivamente voy a chequear algunoss de esos libros.
Francisco Russo no te olvides de "probabilidad y estadistica para ciencias e ingenieria. Walpole" "calculus vol 1 y 2. Apostol" "ecuaciones diferenciales. Denis Zill" 😉
Por cierto saludos tambien desde Bs As (Argentina)😉
Who do you think is better: Messi or Maradona?
10:24 not for passionate people like everyone else here liking and commenting this video.
The more we read the more we crave !
You convinced me, I subscribe !
Greetings from Canada !
"Talking about Maths books is one of the most boring things you can do."
I couldn't disagree with you more.
I’m 14 and I’m ready to do more than high school math
*Mathematics: Its Content, Methods and Meaning*
by: A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev
Dugopolski
A very good effort to educate the people who wants to take interest in mathematics.....keep up the good work
Why, people or viewers are just complimenting her rather speaking on the content...?
I admire u by making a video without sponsor just to help others by the way your eyes are adorable wish u best of luck
Hi. I recommend "Proofs and Fundamentals" by Ethan Bloch, its lecture is very clear and "eye-opening" for a first semester student.
And for Linear Algebra, Gilbert Strang's MIT OCW lectures are excellent, so I bet its book on the subject is worth reading.
for a historical perspective I recommend ' Men of Mathematics ' by E T Bell and ; Mathematics and it's History ' by John Stillwell who is associated with the University at Melbourne .
omg i fall in love with her
Linear Algebra - Hoffman and Kunze, Steven Roman (actually Roman has several pretty solid books on everything from mathematical finance to writing excel macros).
Differential Geometry - Lee
Topology - Munkres -> Hatcher
Algebra - Herstein (or how to teach someone algebra by brutally punishing them)
Analysis - There are no good analysis books. I work in an analysis field. I have yet to find a non-trash book. Bass is terrible too but at least it's free and concise. One day an analyst will figure out that you're allowed to draw pictures and it will be amazing.
You remind me of Pam from ‘The Office’
true!
Sofa King relevant
I solved both volumes of Apostol's Calculus (25-30 per cent of exercises in almost 4 years), and now I'm solving Apostol's Analysis and Differential Equations by George Simmons. I want to achieve a real understandying of certain areas of Maths, studying the correct sequences of contents, without blank spaces. Your election and methods depends on you want to reach. Maybe I could select better books, but I feel confortable with the results I have obtained.
What's your accent from
'Straya
Aussie.
New Zealand, not Australia.
I’m going to go with “Sheila” .. 🇦🇺
The best "book" for a particular course is often a copy of the notes taken by a student in the previous year. If the topics of the course are unchanged then you can fill in gaps in the notes without having to take down all the equations and steps and concentrate better on the lecturer. Not all lecturers hand out printed notes. Even fewer make these available the week before - either handed out or online.
Some courses go a step further and have material produced by more than one person - the lecture given by one, the handouts drafted by another and an online version of the lecture given by a third. This certainly worked well for the early stages of a degree course.
"Математика в техническом университете"
" Смирнов. Курс высшей математики."
" Зорич. Математический анализ"
Yeah! Calculus by Micheal Spivak is what I used back in 1975-76 during my first year in college at the university of Havana Cuba. Other books I used mostly in Cuba were: Mathematical Analysis by Tom M. Apostol, and Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus by Micheal Spivak too. I wish I could remember more books since I do remember to spent one semester, a real semester or about 5 months, learning topics about geometry with an introduction to lineal algebra, and then I took at least 2 or 3 semesters of pure lineal algebra and group theory, but I do not remember the books I used. By the way, I was never able to complete my BA in Cuba, but I did finish it here; however, I can tell that I learned more Math in all my 5 semesters in Cuba than my last 4 short semesters of college, semesters which were no more than 4 months, to obtain my BA in Math.
You are so beautiful. And thank u for this video. It's really useful.
Oh wow, the science and mathematics is so "useful" you had to comment on her looks.
and u had to comment on my comment ?
Brian Tristam Williams What is so wrong about complementing someone's appearance? He didn't do it in a creepy or perverse fashion, and he also addressed the topic of the video, I think his comment was uncommonly polite to be honest. You're just being touchy
Brian Tristam Williams
ruclips.net/video/6AF9QrTJD4U/видео.html
>Great vid, but audio is really soft and coming out the left channel only
Oh wow, the vid is so "great" you had to comment on its sound.
Disgusting.
Recommended readings for the graduate students:
John Bell - Speakable and Unspeakable in Quantum Mechanics
Roger Penrose - The Road to Reality
Kurt Gödel - On Formally Undecidable Propositions of Pincipia Mathematica and Related Systems
Saul Kripke - Naming and Necessity
Omg! Smart and a beatiful girl. The perfect one
Mathematics is a discovery like finding a new bug or seeing fireworks for the first time. I have fought classical teaching methods and strongly despair letting any incomplete paper or grade below maximum. I threw out the books at a academy I was teaching at. The previous teachers gave the students no hope and told them they had no future in their interest.
I felt as an engineer that there is a way to experience math and to challenge the students. I did find a British man’s perspective in MAX PETERS College algebra, A Barrons study guide. I took 8 through 12-year students with his book since the extreme incremental progress and the concise inclusion of everything through to pre-calculus was impressive and exciting. It was not me so much but being a leader and teacher with a great tool, it was possible to get the high school level to get API in their college entrance exam.
For me I could feel correlation of things and fit. It has always been my desire to understand history around mathematics. Einstein wanted to find common relative something in a war-torn world. There seemed no solution but in mathematics and physics there was a window to give hope that there was something that we all had in common down to the smallest things to the largest. That is what drove him, I think. Moving around , different languages and Religious division.
Sometimes people think they need special environment or circumstances to be creative. History shows that in extreme circumstances and great pain was the most accomplished and the most pressure to find answers.
A small boy on a ted talk stated something profound. Stop learning and start thinking and creating. Let the process teach you. At some point and often this is what is needed periodically if not constantly for some. Go to the garden and build a dirt city with friends the creativity and problem solving will amaze you.
The Prussian school system is defective as is grades. Testing abilities and watching what is done with provided tools and materials is a start.
OOps too much. But my passion is in it.
I worked on the premise and in reality for all students to complete all exercises and to get 100% until they get to the next levels. Some methods as Saxon method forced students to re hash and get a mix of previous problem sets to keep in in mind. This was depressing for me and the students can be forced. But math is progression and experience to see a future .
Exercises to go out and measure a building or tree with a stick and a shadow, impress students that life is mathematical not the other way around. Your presentations are attractive and personable. I think teaching in conversational and demonstration method is the way to go.
I would think a game could be created to demand solving math and physics to progress. I mean extensively.
I find you intellectually intimidating.
I don't understand why you would feel intimidated? When I meet someone more knowledgeable or more talented than myself, I feel curious not scared.
@@MeatCatCheesyBlaster That still doesn't explain why someone would feel intimidated. When I meet someone more knowledgeable or skillful than myself, I usually feel curious and look upon it as an opportunity to ask questions and learn something. If that person is jerk or just wants to put me down, well...that's their problem. Usually that sort of person is just hiding behind a fancy title. In reality they're not really as skillful as the title suggests; hence they put others down to discourage them from asking questions and uncovering the fact that they are really just a phony.
Howard Anton's textbook on "Calculus" is excellent...35 years ago when I was a freshman in engineering school and now when I need to brush up. It is for a solid three-semester course, with plenty of special topics.
You are so beautiful tibees
Not boring in the least! Where is the Cambridge list? A worthwhile video.
Zorich - Mathematical Analysis; E. Vinberg - A Course in Algebra. For essential essentials.
(1) Mathematical Methods for Physics and Engineering: A Comprehensive Guide by K. F. Riley and M. P. Hobson (Cambridge University). This book is for Physicists and Engineers at undergraduate level. I believe the 3rd Edition is the latest. This book even has intro to Group Theory and Representation Theory! There is also a Students Solution Manual for 'Mathematical Methods for Physics and Engineering: A Comprehensive Guide'. Also try the following books by Geoff Stephenson (Imperial College, London): (2) Mathematical Methods for Science Students by G. Stephenson. (3) Advanced Mathematical Methods for Engineering and Science Students by G. Stephenson and P.M. Radmore. (4) An Introduction to Matrices, Sets and Groups for Science Students by G. Stephenson. (5) Partial Differential Equations for Scientists and Engineers by G. Stephenson. (6) Special Relativity for Physicists by G. Stephenson and C.W. Kilmister. These G. Stephenson books were based on the mathematics courses he gave to Engineering and Physics undergraduates at Imperial College over the years.