Book with undergrad-level olympiad type problems

[Shivam3013]

Hello everyone! My first post in this seemingly wonderful forum! Anyways, I an currently an undergrad and throughout my high-school career, I have honed my problem-solving skills very well. I have done very well on the olympiads, Putnam, IMC etc. Now that I am an undergrad, I still believe that solving problems is the best way to become better at problem solving. Can anyone recommend me math books with lots and lots of tough undergrad-level olympiad type problems, rather then just basic computational (plug-and-chug) exercises? Mainly for math, but physics/bio/chem/EECS would also be greatly appreciated. Thanks everyone!

 

[jedishrfu]

well there's always: Proofs from The Book

with the best of the best proofs across a wide range of mathematical topics:

https://www.amazon.com/dp/3642008550/?tag=pfamazon01-20

and there's a recent book on Mistakes in Math:

https://www.amazon.com/dp/1616147474/?tag=pfamazon01-20

It doesn't have problems but it shows how errors creep into problems undiscovered until decades later.

My favorite is: Mathematics 1001 by Elwes

https://www.amazon.com/dp/1554077192/?tag=pfamazon01-20

Again no explicit problems, but every topic can open up into a whole range of fun.

For Physics perhaps the Arfken Weber Mathematical Methods for Physicists:

https://www.amazon.com/dp/0123846544/?tag=pfamazon01-20

Following each chapter, is a collection of problems in applied math/physics.

 

[Shivam3013]

Hi; the thing is I have done lots and lots of proof already. I was looking for a few textbooks like Rudin's Principles of Math Analysis which have lots of problems and theorems to proof. I went through the books in the "Math textbook listings" and spending some time with the list made me realize that I would need to complete most of the problems in most of those books! Also, thanks for replying!

 

[Shivam3013]

Also, I would prefer biology and chem books too.

 

[Amrita-Singh]

Try PUTNAM Problems available at MAA Web. if you like difficult undergrad math problems.

 

[Shivam3013]

I am looking for above-Putnam level. But thanks anyways!

 

[verty]

Good luck getting an answer. Your best bet is to do what people have done in the past, apply your skills to a real problem, be it something medical or whatever.

 

[jedishrfu]

Good luck getting an answer. Your best bet is to do what people have done in the past, apply your skills to a real problem, be it something medical or whatever.

I agree, solve some interesting problems then solve some no one has solved.