Books

Some grad students have books

• Some grad students have a space for books they are reading or have read or recommend along the way of study. Here are a list of ones on my radar, either that I’m currently making my way through, will in the very near future, or will during my research for foundational knowledge. Okay, let me be more honest; at the time of my writing this, these are all on my bed or on my working desk, meaning that I’ve fallen asleep while reading them, gotten up again to work through them, rinse, repeat. But I’m determined to get through every single one.
• I thought about sorting them, or putting them in order of “more undergraduate-y” or “definitely graduate”, but I decided not to do this. I don’t think it matters; it’s more of a “some of these are helpful, depending on what your needs are” kind of space.
• Make of it what you will shrug.
• I despise thin books (ie those with a small number of pages, unless it’s Jonathan Livingston Seagull (lol)), but my back hurts from carrying thick ones!
• Oh, you might notice that none of these are programming books. Good! I’m glad you noticed. It’s not an accident :)

Books

• “Prime Numbers: A Computational Perspective” by Crandall, R. and Pomerance C.
• “Rational Points on Elliptic Curves” by Silverman J. and Tate J.
• “How to Solve It” by Polya G.
• “Topological Graph Theory” by Gross J. and Tucker T.
• “Contemporary Abstract Algebra” by Gallian J.
• “Algebra for Cryptologists” by Meijer A.
• “The Arithmetic of Elliptic Curves” by Silverman J.
• “A Transition to Advanced Mathematics” by Smith D, Eggen M and St. Andre R.
• “A Guide to Elliptic Curve Cryptography” by Hankerson D, Menezes A and Vanstone S.
• “Bridging the Gap to University Mathematics” by Gould M. and Hurst E.
• “Extremal Graph Theory” by Bollobas B.
• “Real Analysis” by Cummings J.
• “Abstract Algebra” by Dummit D. and Foote R. (fun fact; they taught at my University while they wrote this)
• “Abstract Algebra” by Hernstein, I. N.
• “Proofs From the Book” by M. Aigner, G.M. Ziegler and K. Hofmann ; thank you Cole and Tyler :)
• “Antifragile: Things that Gain from Disorder” by N. N. N. Taleb
• “Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin” by L. Weinstein and J. Adam
• “Lebesgue Integration on Euclidean Space” by F. Jones
• “Function Theory of One Complex Variable” by R. Greene and S. Krantz
• “Commutative Algebra: With a View Toward Algebraic Geometry” by D. Eisenbud
• “Introduction to Commutative Algebra” by Atiyah and MacDonald
• “Elementary Number Theory” by U. Dudley
• “Mathematical Puzzles: A Connoisseur’s Collection” by P. Winkler
• “Fundamentals of Mathematics, Vol. 1: Foundations of Mathematics: The Real Number System and Algebra” by H. Behnke, F. Bachmann, K. Fladt, W. Suss, H. Kunle, S.H.Gould
• “An Introduction to Abstract Harmonic Analysis” by L. Loomis
• “A Course in Computational Algebraic Number Theory” by H. Cohen
• “Visual Differential Geometry and Forms” by T. Needham (while sitting in on a Diff Alg class that uses notes from the prof)
• “Dancing with Qubits” (with a book club)
• “Quantum Information and Quantum Compression” (with a book club)
• “Matroid Theory” by Oxley (self-study over winter break 2022-2023)

Wish List (will move above once I get them)

• Eisenbud D., Harris J., “3264 and All That: A Second Course in Algebraic Geometry”
• Liu, Q., “Algebraic Geometry and Arithmetic Curves”
• Silverman J., “Rational Points on Elliptic Curves”
• Silverman J., “Advanced Topics in the Arithmetic of Elliptic Curves”
• Halmos P., “Lectures on Ergodic Theory”
• Hidary J., “Quantum Computing: An Applied Approach”
• Arora S., Barak B., “Computational Complexity: A Modern Approach”
• Sipser “Introduction to the Theory of Computation”
• Franceschini M., Ferrari G., “LDPC Coded Modulations”
• Hall B., “Quantum Theory for Mathematicians”
• Neubauer A., Freudenberger J., “Coding Theory: Algorithms, Architectures and Applications”
• Gross B.H., Mazur B., “Arithmetic on Elliptic Curves with Complex Multiplication”
• Cassels J.W.S. “Lectures on Elliptic Curves”

Papers

• I’m not that great at keeping track right now, but I do have a github repo with these.
• Perhaps after I’ve completed everything, I’ll make this public.

For Future

• It would be nice to look back or add to over the years references that were useful to me, so why not start now.

That’s it for now.