Відео

wonderful video! thank you for your insight kaiju mathematics! 😁😁

You could multiply 2/i by i/i to simplify it to 2i/i^2 which is -2i. So the equation becomes 6/(1-2i). Multiply top and bottom by 1+2i to get 6(1+2i)/(1-4i^2) which is 6(1+2i)/5

I recently went back to Community college for math and I didn’t take any trig, I went straight to Calc1 honors, and the prof told me what to review and it was fine.

I’m tackling abstract algebra and analysis next academic year to wrap up my math degree. I’m taking a proof based intro writing class this semester alongside other upper division math. Suggestions for next academic year ?

cool books

Why isn't there a geometry course in community college? Ideally, after introductory algebra, there should be a geometry course, as it greatly helps students with trigonometry, calculus, and linear algebra.

My thought process on how I solved this: Since Kaiju wants a nice solution, I'll try sqrt(x) natural and sqrt(x + 15) natural: we get x = 1. Plugging that in, we get a correct solution. Since the left side is monotonically increasing and the right side is monotonically decreasing, that must be the only solution.

Hi, Math theoxist here, solved some of the other problems! 1) x=3 (true) 2) x=14 (true) 3) x=3 (does not satisfy the equation) 4) x=49 (true) 5) x=64 (does not satisfy the equation) 6) x=9 (does not satisfy the equation) 7) y=(5/2)² (true) 10) x=11 (true) 11) x= 7 (true) That's all I managed to answer!

Wow, you guys spend so much time in choosing a notebook!! We in India just do math on any random paper we get. I usually do math on ultra cheap loose paper, the paper is so bad that it almost feels like tissue paper. If I don't have anything in front of me then I just grab today's newspaper and scribble math problems. I also use a pencil to do math so that if I make mistake I can erase and move on, that way I conserve space.😅

I like how you treat a topic that nobody talks about but that concerns everyone, good content

7:05 i did the same thing because it used to feel more professional

x+√(x)√(x+15)=5 and x≠0 5-x=√(x)√(x+15) 25-10x+x²=x²+15x 25-25x=0 x=1 1+√16=5/√1, this is indeed true. x=1.

How I solved it (without watching the video first, of course): √x + √(x+15) = 5/√x | - √x √(x+15) = 5/√x - √x √(x+15) = 5/√x - x/√x √(x+15) = (5-x)/√x | * √x √(x+15) * √x = 5-x | ()² (x+15) * x = (5-x)² x² + 15x = 25 - 10x + x² | - x² 15x = 25 - 10x | + 10x 25x = 25 | * (1/25) x = 1

Is this before precalculus? I was under the impression that we have to write the restrictions : -5/2, and 6 respectively.

Nice video . If you could also share the link of the books where it’s available at reasonable prices that will be great

It's a shame the publisher can't/won't publish this book in English. The sales would just sky rocket.

Bro I just took few rough notebooks and completed the entire Calculus

I grew up with the book. As a child I saw my young aunts going to school with it. This book got me interested in Algebra. I still have a copy in my bookshelf. There is another book Called Aritmetica de Baldor. It's not well-known. I had a copy of it, too. But I lost it in moving.

Ok Doc,Math has its own language,no need English or Spanish.Do the prombles.

Baldor Algebra, got me interested in mathematics. It's nice to see it in your bookshelf.

Can you recommend some proof books?

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!

Fun problem! The first thing my mind goes to is simplifying those large exponents by subtracting the largest multiple of 4 I can from them (because the powers i of repeat in a cycle of i, -1, -i, and 1) making it ((i*i^3)+2i^2)/i^3. Much easier to deal with from there :)

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. UA-cam 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.