Reviews

From Mathsoc wiki

Contents 1 Junior Freshman 1.1 113 Linear Algebra 1.2 114 Abstract Algebra 1.3 121 Analysis 1.4 141 Mechanics 2 Senior Freshman 2.1 216 ODEs 2.2 224 Geometry 2.3 241 Advanced Mechanics 2.4 Metric and Topological Spaces 2.5 Introduction to number theory 2.6 Elementary projective and algebraic geometry 2.7 Lebesgue integral 2.8 Equations of mathematical physics 3 Sophister courses 3.1 Statistical physics 3.2 Quantum Mechanics 3.3 Differential Geometry/General Relativity

Junior Freshman

113 Linear Algebra

• Elementary Linear Algebra by Howard Anton - I thought this was quite good (though I was young and naive then...)
• Linear Algebra And Its Applications by Gilbert Strang - Kyle and Brendan liked this, I never read it.
• Linear Algebra Problem Book by Paul Halmos - A little more difficult than the course, but closer to Vlad's style, and covering some stuff that's on the course and not in most linear algebra textbooks.
• Matrix Analysis by Johnson and Horn - really comprehensive for matrix stuff, a great reference (especially for the second half of the course). Kind of helpful for Geometry too (224).

114 Abstract Algebra

• Modern Algebra: An Introduction by John Durbin - the only time I've actually ever used this was to write my Logic Gates lab report.
• Abstract Algebra by I.N. Herstein - covers Dr. O'Dunlaing's course much more closely than Durbin - and in (almost) every way, it is superior to Durbin.

121 Analysis

• Calculus by Michael Spivak - great book, not that necessary for the course.
• Principles of Mathematical Analysis by Walter Rudin - intense and compact alternative to Spivak, more than highly recommended.

141 Mechanics

• Richard Crockford's Mechanics Solutions by Richard Crockford - an intuitive and beautiful text, sadly now unavailable.

Senior Freshman

216 ODEs

• The Qualitative Theory of Ordinary Differential Equations by Brauer and Nohel - don't get this book.

224 Geometry

• Analysis on Manifolds by James R. Munkres - Far superior to Spivak because it follows Prof. Simms course more closely - why he doesn't have this as the recommened text, I'll never know.
• Calculus on Manifolds by Michael Spivak - one of the best undergrad books for those serious about Differential Geometry, as it says in the preface, attempt at least all the questions. Casts Differential Geometry in terms of modern notation and consequentially can clash with Prof. Simms' notes.

241 Advanced Mechanics

• Mechanics by Landau & Lifshitz - this book is pretty much the course.
• Classical Mechanics by Goldstein - also quite good in sections.
• Mathematical Methods of Classical Mechanics by V.I. Arnold - very abstract and advanced, one day I'd like to understand it.
• The Classical Theory of Fields by Landau & Lifshitz - good for the special relativity part of the course.

Metric and Topological Spaces

• Introduction to Metric and Topological Spaces by Sutherland, excellent book. Doesn't cover the small functional analysis side to the course, however.

Introduction to number theory

• Lecture notes on Number theory by our very own Prof. Tim Murphy - these are great, 'nuff said. Although if you're thirsty Hardy & Wright is the classic treatment.

Elementary projective and algebraic geometry

• Algebra by Lang - excellant reference for the commutative algebraic part of this.

Lebesgue integral

• The Elements of Integration and Lebesgue Measure by Bartle - excellent and complementary reference to Prof Timoney's course

Equations of mathematical physics

• It's not so bad. I take it all back.
• Any good Bildungsroman

Sophister courses

Statistical physics

• Thermodynamics and Statistical Physics by Greiner, suspiciously close to the course material but not a recommended text... An excellent book to get your head around the course.

• Statistical Mechanics by Kerson Huang, also a very good textbook (possibly with a slightly more advanced approach than Greiner, quite a good complement though).

Quantum Mechanics

• Principles of Quantum Mechanics by Shankar seemed quite nice.

Differential Geometry/General Relativity

• Dr Lazariou seems quite keen on Serge Lang, who has a number of books on differential geometry.
• Sean Caroll's relativity notes were recommended by previous students (though the treatment of some topics may be naive compared to the course notes)
• Geometry of Differential Forms by Morita, I used this previously to understand various parts of differential geometry and liked it, although I haven't used it within the context of studying for this course.