Resources for Students

Resources for Learning

One common question I get from students in my courses (or in tutoring) is where to access material to help their learning process. Whether you're searching for practice problems, conceptual reinforcement, or full-on courses, there is likely something on the internet that can help in your process. Here I'll share some of my preferred resources which I either have used extensively myself or know other people often find to be helpful.

The 3Blue1Brown YouTube Channel is particularly good for conceptual explanations and visualizations in both Calculus and Linear Algebra (he has video series on both topics), and is also just a great math YouTube channel in general.

The Khan Academy is probably the best universal resource for all math content until at least mid-tier college courses (it includes full courses and practice problems completely for free, and is generally very accessible and user-friendly).

Paul's Online Math Notes is a phenomenal, well-fleshed out, and very accessible summary of all the important points from intro algebra, single-variable and multi-variable calculus, and differential equations. This is the best place to look if you just need a quick refresher on some material that you are previously familiar with.

Math Stack Exchange is a great place to look for community sources answers to either broad questions or specific math problems. They have different threads/subsections for practically every subfield of mathematics, and the questions here vary in range from basic computational problems all the way to almost research-level math. If you have a question that other sources on the internet can't help you answer, this is a great place to look or maybe ask it. (There is also the more grown-up Math Overflow for strictly research-level mathematics, designed for experts and professional mathematicians.)

For more advanced math, searching terms from your courses and reading Wikipedia articles is also generally a good way to find information, but admittedly it can be challenging as the articles are often terse and jump straight to the most general/difficult case.

I also highly recommend actually using the textbook you're assigned for a course. In particular, this is the best resource for finding practice problems, and also often contains illuminating exposition that help with those problems (or at least develop the concepts needed to work on them).

Useful Math Tools

Wolfram Alpha is the best free online math calculator that I know of. It can do everything from basic arithmetic to factoring polynomials, computing derivatives, solving multiple integration, dealing with systems of differential equations, finding matrix decompositions, and more. Odds are that if you have a straightforward computational math problem, there is some way you can get Wolfram to calculate it for you.

Desmos is a great, free 2D graphing service that can graph any curve you like that is described in cartesian coordinates, polar coordinates, or parametric equations. It also allows you to save graphs, add sliders for constants, and more.

CalcPlot3D is essentially the 3D analogue of Desmos. This service allows you to plot multivariable functions with ease, so that you can visualize the surfaces by rotating their graphs, looking at level curves, plotting grid lines, and more.

Overleaf is a free online LaTeX editor. LaTeX is universally used by professional mathematicians for typesetting mathematics. It is especially good for making clean documents or presentations, particularly if they contain technical math content. Be warned that there is a bit of a learning curve for typesetting in LaTex, but it is worth it, especially if you intend to continue working in mathematics or a STEM field. Here are a few helpful documents for getting an intro on how to use it (these were given to me by Dr. Nathan Manning at UMD): Scaffold 1, Scaffold 2, Scaffold 3, To Replicate, Basic Template.

Here are a few more LaTeX resources that I find to be especially helpful and cannot help but share: Detexify for finding the TeX command corresponding to any math symbol you can draw; tikzcd-editor for easily making commutative diagrams in TeX without having to know or type the code behind it at all; TeX Stack Exchange is a great place to find answers to any questions you might have about LaTeX; and the LaTeX Wiki for a pretty comprehensive guide on all things TeX related. Also, if you google almost any question about LaTeX, odds are that one of the first links will help solve your problem.

(Here are my preferred LaTeX code templates for making clean looking Problem Sets and Presentations.)