What are the Best Mathematics Books to Read for an Aspiring Mathematician?

[stolz228]

Hello all,

I am new to this forum, and am hoping that I might find some assistance from fellow mathematicians.

I have just completed my first year of college, and find myself with an entire summer in front of me, and yet want to continue my learning. This past year, I took Calc III, Probability, and another Statistics course. In the fall I am planning on taking Lin. Alg, a Statistical Inference class, and a Mathematics of Finance class.

I am wondering if there is a list (around 10 or so) of books that you would all recommend to an aspiring mathematician? It can be a mix of history/theory/whatever, I am just wondering if there are certain works that I should make sure to read while I have all of this free time available.

Thank you

 

[ABarrios]

Hello.
If you'd like to read ahead on Linear Algebra I would suggest this book,
http://www.math.brown.edu/~treil/papers/LADW/LADW.html

As for history and development of Mathematics as well as books on geometry I would suggest the books by John Stillwell.
If you are interested in the development of Calculus (actually analysis), I would suggest The Calculus Gallery.
If you want a head start on Abstract Algebra, look for Herstein's Topics in Algebra or Dummit and Foote's Abstract Algebra. Though I would suggest Herstein for a first time around as it is pretty concise.
Good luck!

 

[Entropee]

I'm not sure if your into physics at all but the Einstein Theory of Relativity by Lillian R. Lieber is basically written in equations no more complicated than tensor analysis; if you have taken calculus 3 you will have no problem reading it, I would highly recommend it. Also the Complete Idiots Guide or the ____ for Dummies may have some good books on linear algebra.

 

[n.karthick]

For Linear Algebra I would recommend you "Introduction to Linear Algebra" and "Linear Algebra and its applications" by Gilbert Strang

 

[jasonRF]

I'll make some suggestions on a lighter side. None of these are textbooks or rigorous books of proofs. They are for fun:

An Imaginary Tale, by Nahin, is a fun book on complex numbers. It is a mix of history and solutions to interesting problems, and the last chapter provides an informal presentation of some complex analysis. Complex analysis is a fun (and useful!) topic with many cute results. This is much easier reading than a textbook, and if you want you can skim the more technical portions - of course you can dive right into them too! I would actually recommend anything by Nahin - he is just fun.

A History of Pi, by Beckmann, is also a fun book with some interesting history and math.

I enjoyed "sync" by Strogatz. Almost made me wish I studied nonlinear dynamics! This book has fewer equations than the previous two, but is really well written and gives a glimpse into the carreer of an academic applied mathematician.

Have a fun summer,

jason

 

[jasonRF]

[EDIT: Dont read this post - it is a duplicate of the above post. sorry! I'm not sure how I did this.]

I'll make some suggestions on a lighter side. None of these are textbooks or rigorous books of proofs. They are for fun:

An Imaginary Tale, by Nahin, is a fun book on complex numbers. It is a mix of history and solutions to interesting problems, and the last chapter provides an informal presentation of some complex analysis. Complex analysis is a fun (and useful!) topic with many cute results. This is much easier reading than a textbook, and if you want you can skim the more technical portions - of course you can dive right into them too! I would actually recommend anything by Nahin - he is just fun.

A History of Pi, by Beckmann, is also a fun book with some interesting history and math.

I enjoyed "sync" by Strogatz. Almost made me wish I studied nonlinear dynamics! This book has fewer equations than the previous two, but is really well written and gives a glimpse into the carreer of an academic applied mathematician.

Have a fun summer,

jason

 

[FieldDuck]

The Man Who Loved Only Numbers - This is a book about Paul Erdos (pronounced Airdish) if you keep on doing mathematics, he's a guy you'll hear about every so often and he's personally one of my favorite mathematicians.

God Created Integers - This book is massive and can be a bit of a read, but there's tons of good information in these pages.

Prime Obsession - This is about the Riemann Hypothesis.

A mathematician's apology - this book is a classic in the math world.

Flatland - not so much a math book as a satire on Victorian society, but does provide good insight on how a 2d object would view a 3rd world.

A mathematical introduction to logic by Enderton - this book requires some knowledge of naive set theory, but I really think it's a great book on logic.

 

[sin2beta]

I would second Strang's Linear Algebra.

Concrete Mathematics by Donald Knuth is very good. It doesn't pull any punches but doesn't require much after calculus. It is subtitled mathematics for computer science, but it is pure mathematics. The problem sets by themselves make it worthy of a look.

A good but still not too intense of a read is Road to Reality by Roger Penrose.