Reddit reviews A First Course in Mathematical Analysis
We found 7 Reddit comments about A First Course in Mathematical Analysis. Here are the top ones, ranked by their Reddit score.
Used Book in Good Condition
The 1st Course In Math Analysis by Brannan
Analysis I by Terrence Tao
Yet Another Intro To Real Analysis by Bryant
Understanding Analysis Stephen Abbott
Elementary Analysis: The Theory of Calculus Kenneth A. Ross
Metric Spaces by Robert Reisel
A Problem Text in Advanced Calculus by John Erdman. PDF
Advanced Calculus by Shlomo Sternberg and Lynn Loomis.PDF
In the grand scheme of math: jack shit. But who's to stop you after 2 months of studying?
What do you know so far? Are you comfortable with inequalities and math induction?
Check out the books below for a nice intro to Real Analysis:
How to Think About Analysis by Lara Alcock.
A First Course in Mathematical Analysis by D. A. Brannan.
Numbers and Functions: Steps to Analysis by R. P. Burn.
Inside Calculus by George R. Exner .
Discrete And Continuous Calculus: The Essentials by R. Scott McIntire.
Good Look.
>My first goal is to understand the beauty that is calculus.
There are two "types" of Calculus. The one for engineers - the plug-and-chug type and the theory of Calculus called Real Analysis. If you want to see the actual beauty of the subject you might want to settle for the latter. It's rigorous and proof-based.
There are some great intros for RA:
Numbers and Functions: Steps to Analysis by Burn
A First Course in Mathematical Analysis by Brannan
Inside Calculus by Exner
Mathematical Analysis and Proof by Stirling
Yet Another Introduction to Analysis by Bryant
Mathematical Analysis: A Straightforward Approach by Binmore
Introduction to Calculus and Classical Analysis by Hijab
Analysis I by Tao
Real Analysis: A Constructive Approach by Bridger
Understanding Analysis by Abbot.
Seriously, there are just too many more of these great intros
But you need a good foundation. You need to learn the basics of math like logic, sets, relations, proofs etc.:
Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers
Discrete Mathematics with Applications by Epp
Mathematics: A Discrete Introduction by Scheinerman
Try these books(the authors will hold your hand tight while walking you through interesting math landscapes):
Discrete Mathematics with Applications by Susanna Epp
Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers
A Friendly Introduction to Number Theory Joseph Silverman
A First Course in Mathematical Analysis by David Brannan
The Foundations of Analysis: A Straightforward Introduction: Book 1 Logic, Sets and Numbers by K. G. Binmore
The Foundations of Topological Analysis: A Straightforward Introduction: Book 2 Topological Ideas by K. G. Binmore
Introductory Modern Algebra: A Historical Approach by Saul Stahl
An Introduction to Abstract Algebra VOLUME 1(very elementary)
by F. M. Hall
There is a wealth of phenomenally well-written books and as many books written by people who have no business writing math books. Also, Dover books are, as cheap as they are, usually hit or miss.
One more thing:
Suppose your chosen author sets the goal of learning a, b, c, d. Expect to be told about a and possibly c explicitly. You're expected to figure out b and d on your own. The books listed above are an exception, but still be prepared to work your ass off.
In case you also want some intro to Analysis(Calculus made a bit more rigorous), here's some:
How to Think About Analysis by Lara Alcock.
A First Course in Mathematical Analysis by Brannan.
I would start with something simple. Open University uses this textbook and it's a very nice gentle introduction to analysis https://www.amazon.com/First-Course-Mathematical-Analysis/dp/0521684242
What do you mean by advanced Calculus? Multivariate Calculus without proofs?
Anyway,
Mathematical Analysis and Proof by Stirling
A First Course in Mathematical Analysis by Brannan
Yet Another Introduction to Analysis by Bryant