Textbook of "introduction to mathematical thinking"

[Mathsway]

Hi everyone
I was wondering does anyone know any good first year undergraduate textbook of 'introduction to mathematical thinking' for self-studying ? thks in advance

 

[ibkev]

I would suggest going through these books in order to get a nice introduction to mathematical thinking, proofs and analysis (which is a revisit of calculus but through the eyes of a mathematician as opposed to someone who might be learning calculus as a tool to solve problems, like an engineer or physicist.)

How to Study as a Mathematics Major, Lara Alcock
https://www.amazon.com/dp/0199661316/?tag=pfamazon01-20

Book of Proof, Richard Hammack (free, frequently recommended for 1st year undergrads and has solutions available for self study)
http://www.people.vcu.edu/~rhammack/BookOfProof/

How to Think about Analysis, Lara Alcock
https://www.amazon.com/dp/0198723539/?tag=pfamazon01-20

 

[Mathsway]

hi ibkev
Thank you for the quick reply. I will certainly check it out.

 

[MidgetDwarf]

Best way, is to due to many proofs.

Try to revisit earlier mathematical content. This is great for two reasons.

(1)Great review of older material. Helps with the eventual GRE. You will find out how much information was not understood the first time.
(2)Since the material is something you are familiar with, you will have easier time reading, and writing proofs of something known.

I learned to read and write proofs from: Reading all of my textbooks throughout my education. Engage the textbook!
I re learned geometry from: Geometry: Moise/Downs, restudied Linear Algebra from Anton( reading, doing, and doing the proofs on my own). I later moved into more advance material.

I cannot stress the trying and doing proofs enough.

The explanation that Moise gives for Existence and Uniqueness is very GOOD. It was something I did not grasp until reading this basic, but good book.