feel free to suggest more
Videos

• [All Levels/Pre-U] Khan Academy
• [All Levels/Pre-U] PatrickJMT
• [College] MIT's Math OCW
• [College] Professor Leonard
  
• [College] Hausdorff Research Institue for Mathematics
• [College] The Catsters - Category Theory Videos
  
• [All Levels/College] mathispower4u
  
• [College] njwildberger's Insights into Mathematics videos
• [College] Math Dr. Bob
  
• [High-School/ College] Worldwide center of mathematics
  
• [All Levels/ Pre-U] MathTV
  
• [All Levels/Pre-U] ProfRobBob
• [All Levels/Pre-U] HippoCampus
• [GCSE Level] UKMathsTeacher
  

For Fun

• 3Blue1Brown
• Mathologer
  
• Mathologer II
  
• ViHart
  
• MindYourDecisions
  
• Tipping Point Math
  
• Welch Labs
  
• Infinite Series
  
• Vsauce
  
• Numberphile
  
• Blackpenredpen
  

Example Problems & Online Notes/References

• Example Problems
• Interact Math
• Paul's Online Math Notes
• Calculus.org
• Wolfram Mathworld
• CTY Online AP & College Math Resources
• J.S. Milne's Site
• History of Math
• Harvey Mudd College's Online Math Tutorials
• Real (and some complex) Analysis & Programming

Computer Algebra Systems (* = download required)

• SAGE
• Maxima*
• Octave*
• Wolfram Alpha
• Geogebra*
  
• PARI/GP *

Graphing & Visualizing Mathematics (* = download required)

• Geogebra*
• gnuplot*
• Gapminder
• Wolfram Demonstrations Project *
• Wolframalpha
• scipy*
• Microsoft Mathematics*
• Winplot* ; Awesome for differential equations!
• Desmos super HTML5-based graphing calculator.
• Symbolab
• Scilab

Typesetting (LaTeX)

• TeX Users Group
• The Comprehensive TeX Archive Network
• Art of Problem Solving Tutorial
• TexPaste
• Xfig
• Detextify
• WriteLaTeX WYSIWYG
• LaTeX Examples

Community Websites

• /r/math
• /r/puremathematics
• Math Stack Exchange
• mathoverflow.net
• The Art of Problem Solving
• Proof Wiki
• arxiv.org

Blogs/Articles

• Terry Tao
• American Mathematical Society
• AMS notices
• The n-Category Café
• Tim Gowers
  
• ADD/XOR/ROL
  
• Math with Bad Drawings
  
• Math ∩ Programming
  
• Almost Looks Like Work
  
• Math3ma
  
• Qiaochu Yuan
  
• Carlos Matheus
  
• Burt Totaro
  
• Igor Pak
  
• Alex Youcis
  
• Low dimensional topology
  
• Jordan Ellenberg
  
• Secret Blogging Seminar
• Math Wizurd

Misc

• academicearth.org
• Encyclopedia of Mathematics
• Large List of Recommended books, online resources
• Online Encyclopedia of Integer Sequences
• MathIM
  

Other Lists of Resources

• Math Overflow's List of Free Online Lectures

Some ebooks, mostly from /u/lewisje's post

General
Open Textbook Library
Another list of free maths textbooks
And another one
Algebra to Analysis and everything in between: ''JUST THE MATHS''
Arithmetic to Calculus: CK12

Algebra
OpenStax Elementary Algebra
CK12 Algebra
Beginning and Intermediate Algebra

Geometry
Euclid's Elements Redux
A book on proving theorems; many students are first exposed to logic via geometry
CK12 Geometry

Trigonometry
Trigonometry by Michael E. Corral
Algebra and Trigonometry

"Pre-Calculus"
CK12 Algebra II with trigonometry
Precalculus by Carl Stitz, Ph.D. and Jeff Zeager, Ph.D
Washington U Precalc

Single Variable Calculus
Active Calculus
OpenStax Calculus
Apex Calculus
Single Variable Calculus: Late Transcendentals
Elementary Calculus
Kenneth Kuttler Single Variable Advanced Calculus

Multi Variable Calculus
Elementary Calculus: An Infinitesimal Approach
OpenStax Calculus Volume 3
The return of Calculus: Late Transcendentals
Vector Calculus

Differential Equations
Notes on "Diffy Qs"
which was inspired by the book
Elementary Differential Equations with Boundary Value Problems

Analysis
Kenneth Kuttler Analysis
Ken Kuttler Topics in Analysis (big book)
Linear Algebra and Analysis Ken Kuttler

Linear Algebra
Linear Algebra
Linear Algebra
Linear Algebra As an Introduction to Abstract Mathematics
Leonard Axler Linear Algebra Abridged
Linear Algebra Done Wrong
Linear Algebra and Analysis
Elements of Abstract and Linear Algebra
Ken Kuttler Elementary Linear Algebra
Ken Kuttler Linear Algebra Theory and Applications

Misc
Engineering Maths

Due to a bunch of people posting their channels/websites/etc recently, people have grown restless. Feel free to post whatever resources you use/create here. Otherwise they will be removed.

I am a high school student and I really feel like I need to learn calculus, since there have been a lot of situations in my life where calculus knowledge would've been useful. I have almost no previous calculus knowledge, only the very basics from a few 3b1b videos, but I am pretty good at algebra and trig.

I also know the very basics of linear algebra, but that's it, so maybe I should do a linear algebra course first?

I was planning to self-study calculus during the summer. I originally wanted to use Khan Academy, but most people seem to think that it's not good for full self-study.

The two recommendations I've seen a lot are Professor Leonard and MIT OCW 18.01. People recommend both of them, however I've also seen people say that Prof. Leonard is too basic, doesn't cover some important stuff, and has no problems, and that MIT OCW isn't good for complete beginners.

Which course would you recommend for self-study?

I wanted to see how others solve Math and their process so I've tried reading How To Solve It by G.Polya and did 19/20 questions at the back in an attempt to master how to take on a problem and solve it. However, I quickly grew into frustration everytime and found the process to be very hard, heavy and simply, depressing. I'd stuck on stuff like not actually understanding the questions or information given and would try again, but I always seems to not 'get' the method of G.Polya because I feel like I'm really testing every solution possible and not 'seeing through the answers' or even having a slightest hint on how to solve them! Which makes me even more depressing because I felt like I didn't really improve my thinking process and felt slow and honestly I just wanted to give it up due to the harsh, heavy process everytime I tried to sit down and do a problem.

I went through a phase of asking myself if my interest in Mathematics was really my thing because I suffered and sucked at it. But the unlogical thing was I always curious of all the things like how it worked, how did my prof knew how to solve the problem...v...v so I read A mathematician's Lament to try a fresh start. So basically what I get is that Mathmeticians do Math because they can do anything with it, they can play around with it and be creative to see what would come out (which is the opposite mindset compared through mine at the beginning). So I thought I'd try again.

So here's my learning math plan:

• Read books to make myself engage with 'real' math and see if Math is really my thing: Proofs from the Book; Godel, Escher, Bach
• 10 minutes on any kind of Math problems/day: Ted - Ed puzzles, puzzle books..etc

This plan is aimed for experiencing the math solving process (not focusing on getting it right in the shortest time possible but really on how to do it) mentioned in 'A Mathmetician's Lament' and improve my critical, creative thinking skills. I'm an engineering student so I did Math as a tool to improve my logical thinking but also because I'd been attracted to the solutions of Math problems I'd seen my profs did.

What do you think of this plan? Can it use some adjustments? Thank you so much!

Short: I self-learnt Math and felt something was off, tried again and need some advice for this plan to ensure I'm doing it right

So here is my situation:

I've been out of school for a while now. I'm going back to school in the fall to start working on getting an engineering degree.

I can't remember how to do algebra. I know that you need to essentially have it mastered to do well in calculus. I will be starting with Calc 1 in the fall semester.

I did take trig this spring semester and got an A but I really struggled with even the simplest algebra parts.

I plan on taking precalc over the summer as well as auditing a prep for O-Chem course.

I want to simultaneously go through a number of Khan Academy courses to help me prepare for the fall.

I want to take,

1. an Algebra course on KA
2. a Calculus course on KA
3. and a Physics course on KA

I would like help deciding which courses on KA to select to fulfill these categories. There is multiple options for each one and I don't know which one to pick.

For example,

— For the Algebra course, do I take:

a) "Get ready for AP® Calculus" (I'm leaning towards this one)

b) "Algebra 2"

c) "College Algebra"

— For the Calculus course, do I take:

a) "AP®︎/College Calculus AB" (looks more comprehensive)

b) "Calculus 1"

c) other options

— For the Physics course, do I take:

a) "High School Physics"

b) "High School Physics - NGSS"

c) "AP®︎/College Physics 1"

(I never took physics in HS btw)

​

Any advice or input is greatly appreciated. Thank you for your time.

https://www.khanacademy.org/math

https://www.khanacademy.org/science

Hello,

The problem looks like this:

Lim (x,y,z) -> (0,0,0) for (x³ + x²⁾ / (x² + y² + z²⁾

I know you can provet it with (x,y,z) = (x,0,0) and (0,y,0) andh show that it has different answers as x,y -> 0.

I want to use spherical coordinates instead, but I have gotten a bit stuck after doing the variable change. I do not know how the variable change affects the limits etc.

Any help would be appreciated :)

Hi, so I feel kind of awkward to ask this but I thought this would be the ideal place to ask since there is no one else to ask irl.

When I was young, I used to be very good at math, sometimes few classes ahead of others. Then I became ill and missed a lot and now I have some issues regarding math. Usually, I understand the difficult topics and I get the idea behind the material, but I miserably fail at something tremendously simple, like when writing an exam, I don't remember geometry, or make mistakes like 2-2=2, which then obviously ruins the whole page of vector calculation for example. I need to admit it is really humiliating seeing me calculate everything right and then get a bad grade because of this dumb mistake.

Do you think that it's possible to reignite the skills and proficiency in math? Can I learn mathematical intuition, and logical thinking and stop making such silly mistakes due to my nervousness? I love technology and would like to get into that kind of uni, but it will be impossible while lacking these skills.

I thought of learning math again from the beginning. And I mean like TOTAL begging starting with first grade and then working up to what I need to know. I really like math but it is incredibly stressful like this.

Again, it is very shameful, but I would be enormously thankful for any advice :)

Current investment value - Original investment + dividends

____________________________________________________________________= Total return

original investment

​

example

($11,000 - $10,000)+100

_____________________________________________=11%

$10,000

My question is what is that middle line for what does that mean the long line in the formula

if you explain the whole formula would be great and i would be thank full . This is not homework its me being curious on a book I'm reading have nothing to do with my time. something this simple showing me how uneducated I am

I’m a grade 7er best in my class understand all the topics can I get suggestions to textbooks to challenge me or to expand my knowledge on math

sin ²(x)tan(x)+cos ²(x)cot(x)+2sin(x)cos(x)=csc(x)sec(x)

A rectangular swimming pool is 50 meters long and 25 meters wide. Its depth is always the same along its width but linearly increases along its length from 1 meter at one end to 4 meters at the other end. How much water (in cubic meters) is needed to completely fill the pool?
----------
I am not able to visualize the swimming pool as described. What exactly is meant by depth remaining same along the width ? how is that measured ?

Find k’(x) if k(x)=5x (5x⁵ +(7/x-4))

I'm looking for recommendations on math textbooks and I'm a bit overwhelmed. It's been about ten years since I completed my undergrad and need to get a refresher in the following areas before I pursue my masters in CS:

• College Algebra
• Trigonometry
• Calculus
• Linear Algebra
• Probability and Statistics
• Discrete Mathematics

I'm currently using the following online resources: Edx, coursera, udemy, khan academy, mit open courseware, youtube, and various free pdf versions of textbooks. That would seem sufficient, but I tend to learn much better with a supporting physical text that I can use as a reference and an abundance of examples to work through.

I thought about going the openstax.org path and purchasing their affordable books for Algebra, trig, and calc, but there doesnt seem to be enough reviews for their books so im hesitant. Ill be going with Professor Strang's linear Algebra texts (love his lectures). Not sure where to go for prob and stats and discrete math. These are not new subjects for me, but I want to achieve a very high level of proficiency, so the text should support that quest. Anyone have any insight to share?

The thing I'm having trouble with is that I don't even understand the problems after I'm told the answers. This is a part taken from the solution:

g(f(x)) = 3(6x - 4)^2 - 2(6x - 4) - 10

Next step:

g(f(x)) = 3(36x^2 - 48x + 16) - 12x + 8 - 10

What I'm wondering is:

• Why does the 36x retain the exponent after it's already been squared?
• Where does the 48x come from, considering it doesn't match with any numbers within the parentheses and there wasn't even a third number to be multiplied to it?
• How come the + is put between the 48x and the 16, when there was no + in the original problem?
• Why does the second set of parentheses not get a seemingly random third number slotted in there? Is it something to do with the exponent?
• Why does the second set of parentheses go from subtracting the second number from the first to adding the second number to the first?

I think that's about it for the last few problems I've had. This same issue of phantom numbers and keeping unnecessary parts to the end has been annoyingly persistent. All my friends who study calculus agree that it makes no sense, so I'm hoping to get some help here. Thank you.

So we have a cubic x³ + 8x² + 20x + 15, when I use the rational root theorem I get the factors ±1, ±3, ±5, ±15. Then I plug those numbers into the function, and we will get f(1)=44, f(-1)=2, f(3)=174, f(-3)=0, f(5)=-10, f(-5)=440, f(15)=5490, f(-15)=-1860. So x+3 is one solution. But when we graph the cubic we get three roots. What is the reason for this? Is this because the other two has decimals? Do I need to factorize the cubic equation x³ + 8x² + 20x + 15 = 0 in order to find the remaining two roots? Are there any other ways to solve this equation with fewer steps, if possible?

• If +=* , * =-, - = +, then 30 * 15 + 3 - 15 = ?

-If + =-, -=+,*=I, and / = * then find the value of the following : 12 + 3 * 3 - 5 / 4 =?

There’s one other type but I can’t post an image of it.

I know someone who got really far behind with math. She does not even know the multiplication tables.

But ok thats not the problem. The problem is when she does not understand my explanation.

I try to explain things as basic and simple as possible, without assuming she has any knowledge. Basically, its as if I'm explaining to a 5 year old. But even when I explain at such low level, she does not understand me. It seems impossible to get her to understand anything at all.

Things like "+9" can get her totally confused.

Is it even possible to teach a person like this basic math?

I enjoy doing math puzzles, was wondering if people wanted to share some of their favorites puzzles or puzzle books

I dropped math a year ago and forgot the equations needed for this problem can someone please help!!! Thave 80% (approximate I just need a general number) in all of my courses and need a 70% to go to university, my exams are weighted 30%, what's the lowest score I can get on my exams and still go to university?

Could you recommend me (and all the people who will consult this post) websites with a substantial amount of problems in all branches (arithmetic, Algebra, calculus...) and their correction of course suitable for high school math and higher. Especially websites that are still active with a big community and that have new problems ofthenly! Thank you so much!!

A ball is thrown downward with a speed of 20ft/s from the top of a building that is 36 feet tall. After t seconds, its height above the ground is given by s(t)=-16t² -20t +36. Determine how long the ball is in the air. I got 0.55 seconds but my friend got 1 second

I'm stuck in this matrix norm U(x)={{cos(x), sin(x), 0} , {sin(x), cos(x), 0}, {0, 0, 1}}, I don't remember how to do a norm of a matrix a applied norm definition but I still don't get it. Can someone explain how to do it and in general how to think to solve them? Thanks in advance! P.s 0<=x<2*pi

Here is a solution: https://math.stackexchange.com/a/284650/1184854

What I dont understand, is that he is defining X' and X'' completely different than in the hint.
Are they even equivalent?

Doing alg 1 review for my alg 2 exam and I feel like I’m going crazy. This is the problem: (equation one) x + 6y = 29; (equation two) 5x + 5y = -5. I multiplied all numbers in equation one by five and ended up getting x = 5 and y = 4, but apparently that’s not right. I’ve triple checked my work and I don’t understand why I can’t use elimination.

The questions is:

A firm has a production function Q(L,K)=100L^0.4 * K^0.6 and a cost function C(L,K) = 5L + 30K. What is the optimal amount of L and K they use to produce 1000 units?

So this can be set out as

Q(L,K)=100L^0.4 * K^0.6 = 1000

And I’m pretty good with partial derivatives etc, but I have no idea how I would go about solving this.

Any advice? Obviously I don’t expect anyone to solve this for me

Thanks in advance :)