Books for the first two undergraduate years

A Listmania! list by J. Oumamar
(REAL NAME)   
 
Problem-Solving Strategies (Problem Books in Mathematics)
1.  Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel
The list author says:
  "You should really already have a copy of this, but I include it anyway because it is an incredible book. Has some use for the Numbers and sets first year course."
£65.76   Used & New from: £24.99
3.7 out of 5 stars  See all reviews (3 customer reviews)

Introduction to Metric and Topological Spaces
2.  Introduction to Metric and Topological Spaces by W. A. Sutherland
The list author says:
  "Decent problem sets and essential to take in Easter term of the first year. Make sure to grasp the inverse function theorem."
Used & New from: £0.01
4.0 out of 5 stars  See all reviews (13 customer reviews)

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Algebra and Geometry
3.  Algebra and Geometry by Alan F. Beardon
The list author says:
  "Transition book from pre-university mathematics; covers half of first year group theory (Orbit stabilizer and isomorphism theorem), spherical/hyperbolic geometry, elementary results in quadratic forms"
£29.24   Used & New from: £17.00
4.3 out of 5 stars  See all reviews (3 customer reviews)

Vector Calculus (Springer Undergraduate Mathematics Series)
4.  Vector Calculus (Springer Undergraduate Mathematics Series) by Paul C. Matthews
The list author says:
  "Easy guide to doing basic computations in vector calculus and intuitive proofs of the results. A book that is quickly outgrown, but still serves some purpose."
£17.47   Used & New from: £9.70
4.9 out of 5 stars  See all reviews (7 customer reviews)

A First Course in Mathematical Analysis
5.  A First Course in Mathematical Analysis by J. C. Burkill
The list author says:
  "After 45 years this is still the best first year analysis book on the market, with more stimulating problems that Rudin. Also written in a "transition to university maths" style."
£28.56   Used & New from: £8.59
4.0 out of 5 stars  See all reviews (2 customer reviews)

Probability: An Introduction (Oxford Science Publications)
6.  Probability: An Introduction (Oxford Science Publications) by Geoffrey Grimmett
The list author says:
  "Covers most of the first year probability course succintly; problem sets a bit lacking though."
£31.14   Used & New from: £10.87
4.8 out of 5 stars  See all reviews (4 customer reviews)

Rings, Modules and Linear Algebra (Mathematics Series)
7.  Rings, Modules and Linear Algebra (Mathematics Series) by B. Hartley
The list author says:
  "Covers the material for the latter half of the rings and modules optional first year course (which you should take!)"
Used & New from: £29.77

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Problem-Solving Through Problems (Problem Books in Mathematics)
8.  Problem-Solving Through Problems (Problem Books in Mathematics) by Loren C. Larson
The list author says:
  "An alternative/complement to Engel with more focus on calculus problems."
£68.75   Used & New from: £43.18
4.0 out of 5 stars  See all reviews (1 customer review)

A First Course in Mechanics (Oxford Science Publications)
9.  A First Course in Mechanics (Oxford Science Publications) by Mary Lunn
The list author says:
  "First year mechanics book. Perhaps a bit lacking in tripos-difficulty and length problems..."
£28.79   Used & New from: £7.59
5.0 out of 5 stars  See all reviews (2 customer reviews)

Introduction to Complex Analysis
10.  Introduction to Complex Analysis by H. A. Priestley
The list author says:
  "Superb book; you will likely cover the first half in a session at the end of the first year and then complete in the second. Make sure to pick up open mapping, maximum modulus and Rouche's theorem."
£26.85   Used & New from: £7.96
4.5 out of 5 stars  See all reviews (8 customer reviews)

An Introduction to Quantum Theory (Oxford Graduate Texts in Mathematics)
11.  An Introduction to Quantum Theory (Oxford Graduate Texts in Mathematics) by Keith Hannabuss
The list author says:
  "Straightforwardly readable coverage of second and part of third year quantum mechanics."
£63.22   Used & New from: £43.39

Elementary Fluid Dynamics (Oxford Applied Mathematics and Computing Science Series)
12.  Elementary Fluid Dynamics (Oxford Applied Mathematics and Computing Science Series) by D. J. Acheson
The list author says:
  "Reasonable book for second and a lot of third year fluid mechanics. Very lacking in challenging problems for the earlier material though."
£38.26   Used & New from: £25.00
4.2 out of 5 stars  See all reviews (4 customer reviews)

A Second Course in Mathematical Analysis (Cambridge Mathematical Library)
13.  A Second Course in Mathematical Analysis (Cambridge Mathematical Library) by J. C. Burkill
The list author says:
  "Many interesting problems and coverage of Analysis II and an alternative view of elementary complex analysis."
£45.35   Used & New from: £23.10
5.0 out of 5 stars  See all reviews (1 customer review)

Probability and Statistics by Example: Volume 1, Basic Probability and Statistics
14.  Probability and Statistics by Example: Volume 1, Basic Probability and Statistics by Yuri Suhov
The list author says:
  "Provides good coverage of first year probability problem solving and second year statistics. Be careful not to abuse this book!"
£40.64   Used & New from: £19.98

Elementary Differential Geometry (Springer Undergraduate Mathematics Series)
15.  Elementary Differential Geometry (Springer Undergraduate Mathematics Series) by A.N. Pressley
The list author says:
  "Covers the latter half of the second year geometry course. Provides quality solutions to exercises if you are having difficulty."
Used & New from: £7.99
4.4 out of 5 stars  See all reviews (5 customer reviews)

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Algebraic Topology
16.  Algebraic Topology by Allen Hatcher
The list author says:
  "The standard text for undergrad algebraic topology. The amount you will cover varies; the first course finishes at homology whilst previous courses had included de Rham cohomology and homotopy theory."
£24.29   Used & New from: £17.00
5.0 out of 5 stars  See all reviews (2 customer reviews)

Representations and Characters of Groups
17.  Representations and Characters of Groups by Gordon James
The list author says:
  "Despite its size it only covers the first half of the course using slightly annoying conventions. Provides extensive experience with finite groups (up to order 1000 in fact!)"
£37.94   Used & New from: £11.57
4.5 out of 5 stars  See all reviews (2 customer reviews)

Principles of Mathematical Analysis (Int'l Ed) (International Series in Pure & Applied Mathematics)
18.  Principles of Mathematical Analysis (Int'l Ed) (International Series in Pure & Applied Mathematics) by Walter Rudin
The list author says:
  "The book most great modern mathematicians learned elementary real analysis from."
£39.71   Used & New from: £25.00
3.9 out of 5 stars  See all reviews (28 customer reviews)

Complex Analysis
19.  Complex Analysis by L. Ahlfors
The list author says:
  "Covers more elementary topics in the Riemann surfaces course. Absolute classic book ."
Used & New from: £14.01

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An Introduction to the Theory of Numbers (Oxford Science Publications)
20.  An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy
The list author says:
  "Covers number theory from first year material to the prime number theorem."
Used & New from: £16.88
4.7 out of 5 stars  See all reviews (3 customer reviews)

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Galois Theory, Third Edition (Chapman Hall/CRC Mathematics Series)
21.  Galois Theory, Third Edition (Chapman Hall/CRC Mathematics Series) by Ian Stewart
The list author says:
  "Slow paced and readable introduction to Galois theory. Covers most of the third year course."
£41.79   Used & New from: £13.30
3.7 out of 5 stars  See all reviews (7 customer reviews)

Linear Analysis (Cambridge Mathematical Textbooks)
22.  Linear Analysis (Cambridge Mathematical Textbooks) by Bila Bollobás
The list author says:
  "Functional Analysis"
Used & New from: £9.12

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Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)
23.  Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics) by J. R. Norris
The list author says:
  "2nd year Markov chains and more!"
£29.99   Used & New from: £14.55
4.0 out of 5 stars  See all reviews (2 customer reviews)

General Relativity
24.  General Relativity by Wald
The list author says:
  "A decent choice of text for third year General relativity. Exercises are perhaps a bit lacking."
£33.30   Used & New from: £17.93
3.8 out of 5 stars  See all reviews (9 customer reviews)

Algebra [1st Edition]
25.  Algebra [1st Edition] by Michael Artin
The list author says:
  "Comprehensive coverage of Algebra for the first two years, but a bit light on Representation and Galois theory."
Used & New from: £26.98

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J. Oumamar
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Qualifications: Oxbridge undergraduate
Last updated: 31/01/2008
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