What are Some Effective Online Resources for Learning Math?

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SUMMARY

This discussion highlights various online resources for learning mathematics, emphasizing the importance of structured materials for self-study. Key resources include the PF Insights blog for mathematics tutorials, Georgia Tech's collection of freely available math textbooks, and numerous YouTube playlists from NPTEL and MIT covering topics such as Real Analysis and Complex Analysis. Additional recommendations include Khan Academy for comprehensive video lessons and the e-book "Seven Sketches in Compositionality" by David Spivak, which introduces applied category theory.

PREREQUISITES
  • Familiarity with basic mathematical concepts such as algebra and calculus.
  • Understanding of online learning platforms and resources.
  • Ability to navigate educational websites and video playlists.
  • Interest in self-directed learning and advanced mathematical topics.
NEXT STEPS
  • Explore the PF Insights blog for mathematics tutorials.
  • Review Georgia Tech's online collection of math textbooks.
  • Watch NPTEL's YouTube playlists on Real Analysis and Complex Analysis.
  • Read "Seven Sketches in Compositionality" to gain insights into applied category theory.
USEFUL FOR

Students, educators, and self-learners seeking to enhance their understanding of mathematics through diverse online resources and structured learning materials.

Greg Bernhardt
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Feel free to use this thread to post online learning resources for math. This may include PDFs, free online books, web apps, problem sets, calculators, tutorials, guides, lessons etc etc.

First stop should be our very own PF Insights blog which hosts many mathematics tutorials
https://www.physicsforums.com/insights

Please don't just post a link, include a description and why it is worthwhile for people to check out.

Thanks!
 
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Mathematics news on Phys.org
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1. Calculus of Complex Variables (MIT)

https://www.youtube.com/playlist?list=PLD971E94905A704482. Functional Analysis (NPTEL)

http://www.youtube.com/playlist?list=PL5022A32B9BCFE3E43. Mathematical Logic (NPTEL)

http://www.youtube.com/playlist?list=PL2EB5662A0D455A814.1 Real Analysis (NPTEL)

version1: http://www.youtube.com/playlist?list=PLbMVogVj5nJSxFihV-ec4A3z_FOGPRCo-

version2: http://www.youtube.com/playlist?list=PLbMVogVj5nJQ1UXrOm7KqTg9UKk6eXRp_4.2 Real Analysis (Harvey Mudd)

https://www.youtube.com/playlist?list=PL0E754696F72137EC5. Complex Analysis (NPTEL)

http://www.youtube.com/playlist?list=PLbMVogVj5nJS_i8vfVWJG16mPcoEKMuWT6. Linear Algebra (NPTEL)

http://www.youtube.com/playlist?list=PLbMVogVj5nJQ2vsW_hmyvVfO4GYWaaPp77. Numerical Methods (NPTEL)

http://www.youtube.com/playlist?list=PLbMVogVj5nJRILpJJO7KrZa8Ttj4_ZAgl8. Abstract Algebra (Harvard)

version 1: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

version2:
http://www.extension.harvard.edu/openlearning/math222/
 
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Ahmad Kishki said:
1. Calculus of Complex Variables (MIT)

https://www.youtube.com/playlist?list=PLD971E94905A704482. Functional Analysis (NPTEL)

http://www.youtube.com/playlist?list=PL5022A32B9BCFE3E43. Mathematical Logic (NPTEL)

http://www.youtube.com/playlist?list=PL2EB5662A0D455A814.1 Real Analysis (NPTEL)

version1: http://www.youtube.com/playlist?list=PLbMVogVj5nJSxFihV-ec4A3z_FOGPRCo-

version2: http://www.youtube.com/playlist?list=PLbMVogVj5nJQ1UXrOm7KqTg9UKk6eXRp_4.2 Real Analysis (Harvey Mudd)

https://www.youtube.com/playlist?list=PL0E754696F72137EC5. Complex Analysis (NPTEL)

http://www.youtube.com/playlist?list=PLbMVogVj5nJS_i8vfVWJG16mPcoEKMuWT6. Linear Algebra (NPTEL)

http://www.youtube.com/playlist?list=PLbMVogVj5nJQ2vsW_hmyvVfO4GYWaaPp77. Numerical Methods (NPTEL)

http://www.youtube.com/playlist?list=PLbMVogVj5nJRILpJJO7KrZa8Ttj4_ZAgl8. Abstract Algebra (Harvard)

version 1: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

version2:
http://www.extension.harvard.edu/openlearning/math222/

I haven't checked most of these lectures, but i guess you can't go wrong with some of the best univesities in the world.
 
A book on advanced integration techniques. It explains how to deal with lots of special functions like zeta, Gamma, eliptic integrals, error function and so on.

https://zaidalyafeai.files.wordpress.com/2015/09/advanced-integration-techniques.pdf
 
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zaidalyafey said:
A book on advanced integration techniques. It explains how to deal with lots of special functions like zeta, Gamma, eliptic integrals, error function and so on.

https://zaidalyafeai.files.wordpress.com/2015/09/advanced-integration-techniques.pdf
the file no longer exists. what book is it?
 
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Another great resource is

Www.mathispower4u.com

It covers math from algebra to first year college of calculus 1,2,3 linear algebra and differential equations
 
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Brock Bidwill said:
Hi, I am new on site. Looking forward for good suggestions.

Welcome to PF!

What about the suggestions in the thread already?
 
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This is very good:

https://www.edx.org/

I followed and passed ''Foundation of data analysis, statistics using R, part1'' online, there are also other math courses on geometry and analysis from the basic to the advanced level. You need to register in order to follow a course ...
Ssnow
 
  • #17
Another great resourse is KhanAcademy. Salman Khan is a great teacher. The site has lots of videos (over 40000) on different subjects about math and other interesting things. And there are a lot of exercises as well to practice your new knowledge.

https://www.khanacademy.org
 
  • #20
Greg Bernhardt said:
David Spivak has a new version of the e-book out:

Seven Sketches in Compositionality: An Invitation to Applied Category Theory
http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf

Interesting. It's 240 pages but aimed at a very wide audience.

The purpose of this book is to offer a self-contained tour of applied category theory. It is an invitation to discover advanced topics in category theory through concrete real-world examples...

The audience for this book is quite diverse: anyone who finds the above description intriguing. This could include a motivated high school student who hasn’t seen calculus yet but has loved reading a weird book on mathematical logic they found at the library. Or a machine learning researcher who wants to understand what vector spaces, design theory, and dynamical systems could possibly have in common. Or a pure mathematician who wants to imagine what sorts of applications their work might have. Or a recently-retired programmer who’s always had an eerie feeling that category theory is what they’ve been looking for to tie it all together, but who’s found the usual books on the subject impenetrable
 

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