What are Some Effective Online Resources for Learning Math?

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In summary: Or a physics student who feels comfortable with electromagnetism but wonders what tensors are all about. Or a biology student who reads Darwin’s Origin of Species but wants to dig deeper. Or a curious machine who wants to know what it means when we say that “programs are data”. Or a graduate student in economics who has no desire to become a category theorist but who wishes to learn what category theory is about because they have some nagging feeling it might be important for their own field. Or even a mathematician who wants to get the gist of what applied category theory is all about, since they suspect that it will shortly start being seen as a “standard part” of the mathematician’s toolkit, just as linear algebra is
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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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This is a collection of open lectures in mathematics and its applications, covering various topics: algebra, calculus, discrete mathematics, history of mathematics, linear algebra, numerical analysis, probability and statistics. I think they are very helpful for those who want to learn mathematics for science and engineering.
http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html
 
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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.
 
  • #8
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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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
 

What are some examples of math learning resources?

Examples of math learning resources include textbooks, online tutorials, educational apps, manipulatives, and educational games.

How can math learning resources benefit students?

Math learning resources can benefit students by providing additional practice, presenting material in different ways, and catering to different learning styles. These resources can also help students develop critical thinking and problem-solving skills.

Can math learning resources be used for all ages and levels?

Yes, math learning resources can be used for all ages and levels. There are resources available for early childhood education, elementary, middle, and high school levels, as well as for college and adult learners.

Are math learning resources expensive?

The cost of math learning resources can vary depending on the type and quality of the resource. While some resources may be expensive, there are also many free or low-cost options available, such as online tutorials and educational apps.

How can teachers incorporate math learning resources into their lesson plans?

Teachers can incorporate math learning resources into their lesson plans by using them as supplemental materials, assigning them as homework or classwork, or incorporating them into classroom activities. Teachers can also use these resources to differentiate instruction and meet the individual needs of their students.

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