Math Problem Books

(Also read – Physics Books for self learning)  How often have you stared at a math (or physics) problem, unsure of where to begin?  Most math books are unusually pedantic and dull – all in an attempt to be more ‘rigorous’.  Screw rigor, I say.  Students are looking for a deeper understanding – lemmas, theorems are certainly not the way to provide that deep understanding.

These books fill this important gap. By providing the first step (where do I start), these problems bring those abstract theorems to life.

Here is a list of my favorite pure math problem books (Algebra, Differential Calculus, Real and Complex Analysis, Linear Algebra and more….) , theoretical (Ph.D. level physics) and mathematical physics problems.  Some of the Web Resources also have solutions to common graduate textbook problems ( Goldstein , Jackson , Griffiths , Peskin Schroder ,  Shankar  , Klauber , Merzbacher).

Pure Math

Mathe

matical

Physics

General Physics  problems (for Ph.D. Qualifiers)

Web Resources

More Pure Math

Slightly Advanced Problems –  graduate level math, but an amazing selection.

Princeton Problems in Physics

 

University of Chicago – Graduate Problems in Physics

 

PhysicsPages

Counterexamples in Analysis

GoldStein Solutions

Problems in Group Theory

Perfect for the budding high school or college math student. There’s no comparison to the ‘Green’ and the companion ‘Red’ Book problems.

J.D. Jackson Solutions

100 Great Problems of Elementary Mathematics

Bernoulli, Cauchy, Euler…Solar, Lunar Eclipses, Brightness of Venus…The journeys in here are priceless. Don’t let the word ‘elementary’ fool you.

Perfect for the budding high school or college math student. There’s no comparison to the ‘Green’ and the companion ‘Red’ Book (slightly harder than the Green Book) problems.

Think you understand relativity? Try this book for size. Some of the problems in here are research topics in their own right. What an amazing selection!

Complex Functions, Harmonic and Analytic Functions are the lifeblood of physicists and other mathematical sciences. This translation (from Russian) is probably the greatest collection of complex analysis problems, with solutions.

 

For those demanding graduate physics courses, this might be a good resource. Solving J.D. Jackson’s Electrodynamics problems was always a painful experience (though I did manage to eke out an A in that course). This book helped me with some of the tougher expansions.

A fun collection of problems

Summary

This list was not created overnight. Over a period of two decades, these books were part of the additions to my personal library.

Please comment if I am missing your favorite math problem book (or mathematical physics problem book) ! Also see Rare Finds in Relativity

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