# What are some good university level texts with solutions?

What are some good university level texts for which the exercises have solutions? Any textbooks, books, lecture notes etc. whose problems and exercises have solutions would be great. Please indicate if these are full solutions, partial solutions or just hints.

Some good examples that I have seen are the books by Prof. Robert Ash at https://faculty.math.illinois.edu/~r-ash/ which include full solutions.

Please note: This post is not a discussion over whether or not you support the inclusion of solutions, or your opinion on the inclusion of solutions, it is merely asking for sources that have exercises with solutions.

As noted above the website of Prof. Robert Ash https://faculty.math.illinois.edu/~r-ash/ has books on the following topics, all with full solutions

• Abstract algebra
• Algebraic number theory
• Commutative algebra
• Complex variables
• Statistics
• Real variables with basic metric space topology
• Basic probability theory

The excellent site of J.S. Milne https://www.jmilne.org/math/index.html has lots of notes on a wide range of topics, some of which are graduate level and above. The following course notes have hints/partial solutions to every exercise; to quote Milne "These solutions fall somewhere between hints and complete solutions. Students were expected to write out complete solutions"

• Group theory
• Fields and Galois theory
• Algebraic geometry
• Algebraic number theory
• Class field theory
• Complex multiplication

There is also a page at http://www.exampleproblems.com/wiki/index.php/Main_Page which contains some information and exercises with full solutions covering the following topics

• Basic algebra
• Calculus
• Ordinary differential equations
• Partial differential equations
• Fourier series

Paul's online math notes at http://tutorial.math.lamar.edu/ have lots of useful content including some cheat sheets, various notes and reviews. The following lecture notes have practice problems which come with full solutions and assignment problems which have no solutions

• Algebra
• Calculus I
• Calculus II
• Calculus III

Gerstein's "Introduction to mathematical structures and proofs" has hints (and some solutions) to the odd numbered exercises.

Hefferon "Linear Algebra" has full solutions.

Lee's "Abstract Algebra" has solutions to the odd numbered problems and is currently (April 2020) available for free download from Springer due to the coronavirus situation.

Gamelin, Greene "Introduction to topology" contains full solutions to selected exercises.

The "Elementary Topology: Problem Textbook" has full solutions, plus proofs for the theorems are presented at the end of the main text so that readers can attempt them independently if they desire.

"Fundamentals of General Topology: Problems and Exercises" by A.V. Arkhangel'skii and V.I. Ponomarev has full solutions.

Sutherland's book "Introduction to Metric & Topological Spaces" has solutions to the odd-numbered exercises available to students on the publisher's website https://global.oup.com/booksites/content/9780199563081/ and full solutions available to lecturers who register for an account.

Bona's "Introduction to Enumerative and Analytic Combinatorics" has full solutions.

Graham and Knuth's "Concrete Mathematics: A Foundation for Computer Science" has full solutions to all exercises, except the "research exercises".

"Calculus with applications" by Lax and Terrell has solutions to selected problems and again is currently (April 2020) available for free download from Springer due to the coronavirus situation.

Dineen's "Multivariate Calculus and Geometry" has "Solutions, answers, hints or relevant remarks to selected exercises" and again is currently (April 2020) available for free download from Springer due to the coronavirus situation.

Laczkovich, Sós "Real analysis" has both hints and solutions, but only for selected exercises and again is currently (April 2020) available for free download from Springer due to the coronavirus situation.

"Problems in Real Analysis A Workbook with Solutions" by Aliprantis and Burkinshaw has over 600 problems and solutions based on the book "Principles of real analysis" by the same authors.

Brezis "Functional Analysis, Sobolev Spaces and Partial Differential Equations" contains partial solutions.

Aubin "A course in differential geometry" has (I think) full solutions.

"Geometry of Differential Forms" by Morita has full solutions.

Many (but not all) of the Cornerstone Series have partial solutions. Those which have partial solutions include "Basic algebra" "Advanced algebra" "Basic real analysis" "Advanced Real Analysis" "Partial Differential Equations" "Distributions: Theory and Applications".

There's also proof wiki https://proofwiki.org/wiki/Main_Page which contains many standard (and non-standard) step by step proofs covering a wide range of topics.

Math counterexamples http://www.mathcounterexamples.net/ is as the name suggests a huge repository of useful counterexamples.

Tricki http://www.tricki.org/ is a wiki style problem solving resource.