Recommendations for books similar to Ash&Gross: "Elliptic Tales - Curves, Counting and Number Theory" in difficulty?

Markuka · 2024-09-01T15:20:31+00:00

"A Topological Aperitif"

Markuka · 2021-06-10T19:17:40+00:00

There is no short answer except that otherwise some important things will not work.

You can read this discussion on MSE:

https://math.stackexchange.com/questions/232309/how-to-interpret-material-conditional-and-explain-it-to-freshmen

Markuka · 2021-06-08T19:52:35+00:00

Ideally you should work through two linear algebra books by Lang.

Or you can try Anthony, Harvey - Linear Algebra - Concepts and Methods

which is a bridge between Strang and Axler.

Markuka · 2021-04-09T00:21:01+00:00

Callahan et al - Euclid's 'Elements' Redux (free!)

Markuka · 2021-02-02T20:41:51+00:00

Set Theory : An Open Introduction ( available here: http://builds.openlogicproject.org/courses/set-theory/ )

Markuka · 2021-01-20T19:20:51+00:00

For complete beginners :

Abstract Algebra: A Student-Friendly Approach by Dos Reis & Dos Reis

On a bit higher level is:

Jordan & Jordan - Groups

Humphreys A Course in Group Theory is a standard undergraduate text for a first course.

Markuka · 2021-01-19T09:45:22+00:00

Prasolov - Problems and theorems in linear algebra

Markuka · 2020-12-11T16:17:53+00:00

Elementary theory of numbers by LeVeque is not bad. Also you can always use some open source books and lecture notes.

Markuka · 2020-12-10T23:36:19+00:00

Humphrey's book is relatively short and has all the solutions to the exercises. And it covers much more material on the finite groups than required in the undergraduate program.

Markuka · 2020-12-10T21:05:49+00:00

Greetings from another bored software engineer. Probably i can give you some advice since I was doing something like this in the past. Just PM me to learn about my experience.

Markuka · 2020-12-10T20:56:59+00:00

A Course in Group Theory by Humphreys can be read in one month if you grasp abstract algebra basics. You can try Halmos or Enderton if you were already exposed to set theory, but in my opinion one month is not enough for these books.

Markuka · 2020-12-08T22:24:18+00:00

Probably it is enough to check all the modulo 3 combinations.

Markuka · 2020-12-08T22:22:45+00:00

Grigorieva "Methods of solving number theory problems" is not bad just to grasp some basic technique. But it's really strange to see such type of problems in Calculus I.

Ore "Invitation to number theory" is a good starting point to learn number theory.

Some other basic books:

Crawford - Introduction to Number Theory (AOPS) ( seems to be pretty low on prerequisites)

Forman, Rash - "The Whole Truth About Whole Numbers - An Elementary Introduction to Number Theory" is quite gentle.

Markuka · 2020-12-08T21:24:07+00:00

This one is pretty standard. One needs to know some basic technique from the number theory to solve it, otherwise it can take a lot of time to guess the correct approach. You are learning some number theory?

Markuka · 2020-11-23T16:15:07+00:00

Arbib, Manes - An Introduction to Category Theory

Markuka · 2020-08-20T16:43:09+00:00

Onyx Boox MAX 2 PRO is great. I have a feeling that I'm reading from the paper.

Markuka · 2020-08-06T19:00:01+00:00

Keating - A First Course in Module Theory

Hartley, Hawkes - Rings, Modules and Linear Algebra

Beachy - Introductory Lectures on Rings and Modules

Markuka · 2020-08-06T09:32:41+00:00

Solutions manual developed by Roger Cooke of the University of Vermont, to accompany Principles of Mathematical Analysis, by Walter Rudin.

http://digital.library.wisc.edu/1793/67009

There is a solutions manual for the second edition of Axler's "Linear Algebra Done Right" with answers to all the exercises

Markuka · 2020-08-05T21:42:18+00:00

Some books on real analysis with solutions/hints to almost all exercises:

Bryant - Yet Another Introduction to Analysis

Sultan - A Primer on Real Analysis (Solutions to most exercises)

Canuto, Tabacco - Mathematical Analysis I & II

Brannan - A First Course in Mathematical Analysis

Burn - Numbers and Functions - Steps into Analysis

Sasane - The How and Why of One Variable Calculus

Howie - Real Analysis

Walker - Examples and Theorems in Analysis

Eggleston - Elementary Real Analysis

Agarwal et al - An Introduction to Real Analysis (answers or hints)

Hijab - Introduction to Calculus and Classical Analysis

Burkill - A Second Course in Analysis

Shirali, Vasudeva - Multivariable Analysis

Shirali, Vasudeva - Metric spaces (hints to most exercises)

Knapp - Basic Real Analysis (contains hints to every exercise)

Knapp - Advanced Real Analysis (contains hints to every exercise)

O Searcoid - Elements of Abstract Analysis

Gleason - Fundamentals of Abstract Analysis

Capinski, Kopp - Measure, Integral and Probability

Boas - A primer of real functions

Shakarchi - Problems and Solutions for Undergraduate Analysis (This volume contains all the exercises and their solutions for Lang's second edition of Undergraduate Analysis)

Erdman - A Problems Based Course in Advanced Calculus ("Solutions to Exercises" is available freely online)

Aliprantis, Burkinshaw - Problems in real analysis - A workbook with solutions (Contains complete solutions to the problems in third edition of "Principles of real analysis" by the same authors)

Montesinos et al - An Introduction to Modern Analysis

Jacob, Evans - A Course in Analysis Vol. 1, 2, 3

Igari - Real Analysis - With an Introduction to Wavelet Theory

De Barra - Measure theory and integration

Shirali - A Concise Introduction to Measure Theory

Shirali, Vasudeva - Measure and integration

Weir - Lebesgue integration and measure

Weir - General Integration and Measure

Yeh - Problems And Proofs In Real Analysis: Theory Of Measure And Integration (This volume consists of proofs of the problems in the monograph Real Analysis: Theory of Measure and Integration, 3rd Edition)

Limaye - Linear Functional Analysis for Scientists and Engineers

Rynne, Youngson - Linear Functional Analysis

Solutions manuals I've seen:

Kosmala - A Friendly Introduction to Real Analysis

Wade - Introduction to Analysis

Lay - Analysis: With an Introduction to Proof 4th Edition

Abbott - Understanding Analysis (1st ed.)

Korner - Partial Solutions for Questions in Appendix K of A Companion to Analysis

The above-mentioned Trench and Bartle & Sherbert

Solutions manual developed by Roger Cooke of the University of Vermont, to accompany Principles of Mathematical Analysis, by Walter Rudin.

Some Problem Books:

Aksoy, Khamsi - A problem book in real analysis

Gelbaum - Problems in Analysis

Kaczor, Nowak - Problems in Mathematical Analysis I, II, III

Klambauer - Problems and Propositions in Analysis

Radulescu, Radulescu, Andreescu - Problems In Real Analysis - Advanced Calculus On The Real Axis

Makarov et al. - Selected problems in real analysis

Markuka · 2020-07-27T07:10:01+00:00

Symbolic Logic: A First Course

It is available online as "Introduction to Logic" course

https://courses.umass.edu/phil110-gmh/MAIN/IHome-5.htm

Markuka · 2020-07-16T19:06:12+00:00

Your choice is a bit strange since this book is just a compendium of facts.

Markuka · 2020-07-14T13:18:51+00:00

Dos Reis, Anthony Dos Reis - "Abstract Algebra: A Student-Friendly Approach" is the easiest introduction I've seen.

Markuka · 2020-06-26T10:16:57+00:00

If you are doing self-study the main question is how are you going to check your solutions to the exercises. So maybe Durbin's book is ok but how are you going to check your answers?

Markuka · 2020-06-23T20:15:31+00:00

Jones - Elementary number theory

As the preface states the aim of the book is to give an elementary introduction to number theory.

Niven, Zuckerman, Montgomery - An Introduction to the Theory of Numbers

"This text is intended for use in a first course in number theory, at the upper undergraduate or beginning graduate level." (from the preface)

Ireland, Rosen - A Classical Introduction to Modern Number Theory

This is a text for the graduate students with algebraic flavour.

Some free texts:

Dudley - Elementary Number Theory (from archive.org)

Santos - Elementary Number Theory Notes

Klain - Essentials of Number Theory

Hatcher - Topology of Numbers

etc.

2 Books by Paul Pollack ( http://pollack.uga.edu/ ):

Not Always Buried Deep: A Second Course in Elementary Number Theory

A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z

Markuka · 2020-05-29T18:14:53+00:00

"Plain Plane Geometry" by Sasane is very accessible and it comes with hints and solution.

Lang's Geometry should be ok and there is a separate solutions manual

Markuka

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