Books for the first two undergraduate years

A Listmania! list by J. Oumamar
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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."
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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."
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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"
£26.40   Used & New from: £15.00
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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."
£31.67   Used & New from: £17.00
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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."
£22.79   Used & New from: £3.99
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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."
£30.03   Used & New from: £9.97
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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!)"
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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."
£44.64   Used & New from: £28.22
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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..."
£28.49   Used & New from: £9.56
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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."
£26.38   Used & New from: £17.50
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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."
£55.86   Used & New from: £44.23
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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."
£36.96   Used & New from: £20.00
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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."
£46.55   Used & New from: £32.58
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Probability and Statistics by Example: Volume 1, Basic Probability and Statistics: Basic Probability and Statistics v. 1
14.  Probability and Statistics by Example: Volume 1, Basic Probability and Statistics: Basic Probability and Statistics v. 1 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!"
£35.15   Used & New from: £28.19
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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."
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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."
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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!)"
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Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics)
18.  Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin
The list author says:
  "The book most great modern mathematicians learned elementary real analysis from."
£34.49   Used & New from: £11.96
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Complex Analysis
19.  Complex Analysis by L. Ahlfors
The list author says:
  "Covers more elementary topics in the Riemann surfaces course. Absolute classic book ."
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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."
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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."
£35.19   Used & New from: £28.50
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Linear Analysis (Cambridge Mathematical Textbooks)
22.  Linear Analysis (Cambridge Mathematical Textbooks) by Bila Bollobás
The list author says:
  "Functional Analysis"
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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!"
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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."
£30.80   Used & New from: £26.58
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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."
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Author
J. Oumamar
(REAL NAME)   
Qualifications: Oxbridge undergraduate
Last updated: 31/01/2008
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