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i really like the concepts app for iPad. gives you a nearly infinite canvas so you aren't bounded by the size of the notebook page you're on. i use a dotted background so i have something to line up against but it isn't in my way if i want to do something freeform. my pocket notebook is just printer paper cut in half and then folded again in half. makes for an a6 pocket notebook. and half a ream of paper'll get me a couple dozen of them. you can even print custom pages if you've got the need. i either staple it or run it through the sewing machine to secure the spine.

I can never do these because the first step I always subconsciously take (which is wrong) is dividing x^2 by x^2 and so rewriting it without those and with a 1 in front of the first numerator and I know it isn’t multiplication so I can’t do it but I just do 😂

Awesome stuff

My first thought was to think of it as an augmented matrix and use row operations:)

You are awesome! I’m a current senior in an applied and computational mathematics major and watching how understanding you are with the different walks of life who come through your classes is truly inspiring. You definitely called me out when you talked about the skipping class! My goal for my last two terms of undergrad is to not miss a single class! Cheers!

I haven't watched the video yet but have managed to figure out the solution to the problem in around 3-4 steps. Not to take anything away from your video but I find my method much faster and intuitive. Some Background on Imaginary Numbers: i goes in cycles of four, i, -1, -i, and 1. So for any value n, i^n must be i^(n mod 4) [mod is just the remainder]} 1. [i^(25 mod 4) * i^(31 mod 4) + 2i^(10 mod 4)]/i^(15 mod 4) 2. [i * (-i) + 2i^2]/-i 3. [-(-1) - 2]/-i => 1/i 4. 1/i * i/i => -i I would really like to hear your thoughts on the way I approached this problem. Thanks!

solid work man.

Why cant i do i^46 = (i^4)^11.5

he he. 3:34 algebraic division was the part in which I struggled more when I was a kid in junior high. now, many years later, I took this amazing book again, and with patience and discipline I managed to understand and solve the exercises about division one by one. Discipline and practice is all that you need to become proficient at math in general. And solid foundations.

Would you mind doing a video of Martin-Gay’s Geometry and/or Blitzer’s College Algebra? Once I finish Blitzer’s Algebra for college students I plan on tackling College Algebra. I’m on chapter 3 of the geometry book.

Based on one of your previous videos, I picked up Mathematical Ideas. I was able to pick up the student edition, instructor edition and instructor’s solution manual for a reasonable price. That book is really densely packed with mathematics! It overwhelming! I’ve decided (today) to align the topics with what I’m doing in my self study. Also, finding a copy of Elayn Martin-Gay’s Geometry (for under $100) took me forever!

Writing in a book, even with pencil, is sacrilege!

Do you know any books that are obsessive at trying to teach mathematical concepts in extremely visual, palpable and kinesthetic ways? Not only that but books that solve some problem in as many ways as possible yet they reach the same correct result. RUclips is highly lacking in recommendations like that. Thanks so much.

The community college im about to go to is amazing for physics.

I'm not a math major, but I started with college Algebra about 10 years ago when I first went to college. I only needed up to precalculus for an associate of businesses. I recently decided to go back for science, so I knew i needed to sharpen my math skills. I was going to retake precalculus as an 8 week accelerated course and I realized when I was doing the first assignment that I forgot so much of what I was expected to already know. I attempted to take college algebra, but the class was full so I went all the way back to intermediate algebra last semester. I decided that I will just take college algebra this semester. I'd rather just build myself back up than struggle, trying to jump right back where I left off years ago.

Wouldn't it be better to first expand the (x-1)³ term, since we also kind of still do it in the end, so it's just faster to turn it into a polynomial and wouldn't even have to use the product rule!

literally just beauty😮‍💨

In Brazil most selective universities start undergraduate math courses with calculus. Is it different in the US?

Thanks for the overview of the topics in the books. I am self-taught in data-science, I have to learn statistics, probability and math from scratch to college level) Your review helped me better understand what to study and in what order.

I was wondering if I am alone in this world having a complete Calculus and differential equations text book library started collecting them in 1978.

I've been re-learning Maths for a while now, and it surprises me that the most basic math, arithmetic, is called "pre-algebra", as if "arithmetic" is too pitifully basic to be in the title LOL. // I have that Baldor book too, it's good!

That last one, dude, YOU got it wrong. Read the instructions again.

Do they have an English translation?

I love solving this along with you as I watched!

Very cool! Keep up the good work.

I just got a 53/100 on my math final yesterday. College algebra and trigonometry.

Good story!

I'm taking CS at my first semester of college, and I've already burnt through 5 notebooks and it's been really inconvenient trying to go back to my notes or look for past problems. I hope I can get an Ipad soon.

Also x is not 1 x is not -2,else you can not divide

Thoroughly explained. Love this. ❤

Complete the Square would have been quicker.

Saw the thumbnail and immediately solved it + 500 aura

So, I have to ask,...what Real World situation would create the need for this formula and it's solution?

You could also solve this using the “Complete the Square” method. Starting from x^2 - 2x + 1/4 = 0, we can move the 1/4 to the right hand side. If we let b=2 (from the coefficient on the left hand side term), then we can add to both sides (b/2)^2 meaning we essentially add 1 to both sides. Hence we have the equation: x^2 - 2x + 1 = 1 - 1/4 We notice that the left hand side of the equation is in an expanded form of a square. If we condense it, we have: (x - 1)^2 = 3/4 Simplifying, we get: x - 1 = sqrt(3)/sqrt(4) x - 1 = sqrt(3)/2 x = 1 + sqrt(3)/2; 1 - sqrt(3)/2 And this is the most simplified form of the solution presented in the video. Well done, Kaiju!

I love your channel. I'm an older adult who has always wanted to return to the study of mathematics once I became a bit older and had some more free time. Thankfully, that time has arrived, and I'm enjoying every minute of it. I'm planning to work my way through the entire sequence of courses that make up an undergraduate mathematics education, savoring every step along the way with no pressure and no need to rush. With any luck, I'll be able to keep pushing myself and maybe even undertake graduate studies in mathematics one day. In any event, keep up the great work with your channel! 🙂

you look like sheldon cooper

Hello, I'd need your advice on math learning, do you have a mail I could write to? Thanks a lot!

Excellent review thanks

Don't you have textbooks on more advanced math subjects?

Cool! 🎉🎉🎉

you saved me

My method was to seperate 8^3x-5 to 8^3x/8^5 which is equal to 13 then i simply multiplied 13 and 8^5 which gave me 425984 after this, i did log 8^3 both sides to get rid of 8^3x and get only x after this, it was just log 8^3 (425984) u used a rlly interesting method tho :D

You could seperate it into: (8^x)(8^x)(8^x)(8^-5)=13 Let a variable y=8^x (8^-5)y³=13 And then solve for y and letting the solution = 8^x

8^(3x-5) = 6227020800?

so x has 4 real solutions?

could you also say x = (log13/log8+5)/3 ?

isn't x =187/90

why not just simplify to log base 8 of 13 +5 divided by 3, thats what i did

I’m also a fan of collecting textbooks mine is mostly Anatomy though!

A combo. The iPad with good notes to do all notes and practice, and a normal notebook where you only write math concepts, theorems and laws and perhaps one example problem to accompany each. This works for me.