*Towards a new HR*and

*Secondhand Standards*. It will explain a bit more about the feasibility and philosophy behind this post.

All this post is meant to do is propose a list of texts that are rigorous and provide a well-rounded foundation in Undergraduate Mathematics. Be forewarned that it leans more towards Algebraists than Topologists. Lest anyone think I'm a total quack I plan to eventually work through all of these myself and have been researching which math texts are good on and off for a few months now. Autodidacticism (to my thinking) doesn't work without good books. I also have a list for an Undergraduate Computer Science education but I'm not quite done with it.

There are 20 texts and their total cost is about 700 dollars when they're bought used off Amazon. This also covers most all of what you would learn in High School Mathematics. Click on the book's title to get forwarded to it's Amazon.com page. The ordering of the list loosely conforms to increasing difficulty but it is not a recommendation as to structure. I'll probably go into such details at a later date.

What is Mathematics? by Richard Courant and Herbert Robbins

How to Solve It by G. Polya

How to Prove It by Daniel Velleman

Algebra by I.M. Gelfand and Alexander Shen

Functions and Graphs by I.M. Gelfand, E.G. Glagoleva and E.E. Shnol

The Method of Coordinates by I.M. Gelfand, E.G. Glagoleva and A.A. Kirilov

Trigonometry by I.M. Gelfand and Mark Saul

Calculus by Michael Spivak

Discrete Mathematics and it's Applications by Kenneth Rosen

Introduction to Probability by Dimitri Bertsekas and John Tsitsiklis

Introduction to Linear Algebra by Serge Lang

Linear Algebra by Serge Lang

A Mathematical Introduction to Logic by Herbert Enderton

A Classical Introduction to Modern Number Theory by Kenneth Ireland and Michael Rosen

Topology by James Munkres

Topics In Algebra by I.N. Herstein

Algebra by Michael Artin

Ordinary Differential Equations by Morris Tenenbaum and Henry Pollard

Principles of Mathematical Analysis by Walter Rudin

Concrete Mathematics by Ronald Graham, Donald Knuth and Oren Patashnik