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MA140 Content


This module gives a rigorous introduction to some of the principles of mathematical analysis that are essential in most aspects of modern mathematics.


  • The real numbers: Supremum and infimum, completeness axiom, rational and irrational numbers
  • Sequences: Convergence, algebra of limits, Cauchy sequences, monotonicity, subsequences, Bolzano-Weierstrass Theorem
  • Series: Convergence and divergence, tests, absolute convergence, rearrangements, the number e
  • Continuity: Functions, formal definition of continuity, continuity and limits, algebra of continuous functions, the intermediate value theorem and the extreme value theorem


In addition to mastering the contents listed above, by the end of the module students will be able to understand and write formal mathematical sentences (aided by symbolic quantifiers).


D. Stirling, Mathematical Analysis and Proof, 1997
M. Spivak, Calculus, Benjamin
M. Hart, Guide to Analysis, Macmillan. (A good traditional text with theory and many exercises)
G.H. Hardy, A Course of Pure Mathematics, CUP