Question

what is the best reference book for math in b.sc 1st year??

Answer 1

Before specifying the names, I would like to emphasise that a Math student must read a book from page 1 (right where the author’s notes are) till the end (appendix and bibliography). This gives an insight into the subject, and also makes one aware of the pattern that the book follows.

Now coming back to the question, the books depend on the papers that you take in your 1st year. Following are some suggestions based on personal experience:

Real Analysis:

Real Analysis by Bartle and Sherbert

Principles of Mathematical Analysis by Rudin

Modern Algebra:

Contemporary Abstract Algebra by J.A. Gallian

Abstract Algebra by Dummit and Foote

Linear Algebra:

Linear Algebra by Friedberg, Insel and Spence

Linear Algebra by Hoffman and Kunze

Differential Equations:

Differential Equations by SL Ross

Elementary Differential Equations by Edwards and Penney

Numerical Methods:

Numerical Methods for Scientists and Engineers by Jain, Iyengar and Jain(watch out for the inadvertent error here and there in this book though!)

Metric Spaces:

Metric Spaces by Shirali and Vasudeva

Topology of Metric Spaces by Kumarasen

Complex Analysis:

Complex Variables with Applications by Brown and Churchill

I personally think that barring a few papers here and there, these books will sail you through not just your 1st year, but also through the entire BSc.