Table of Content
Geometry: Preliminaries, Some properties of triangles, Triangles and circles, Concyclic points, The orthocenter of a triangle, Internal and external bisectors, The theorems of Ceva and Menelaus, Analytical methods, Finding loce by analytical methods, More properties of circles, Vector methods, Review exercise, Answers, Index Statistics and Probability: Introduction, Cumulative distribution functions, Geometric and exponential probability, Linear combinations of random variables, Some properties of normal probability, Hypothesis testing, Large sample distributions, The central limit theorem, Hypothesis testing with discrete variables, Errors in hypothesis testing, The t-distribution, Confidence intervals, A survey of probability distributions, Chi-squared tests, Review exercise, Appendix: some supporting mathematics, Answers, Index Sets, Relations and Groups: Introduction, The language of sets, Equivalence relations, Functions, Binary operations and groups, Some examples of groups, Subgroups, Isomorphisms of groups, The algebra of sets, Review exercise, Answers, Index Series and Differential Equations: Introduction, Summing finite series, Infinite series, Tests for convergence, Series and integrals, Infinite integrals and infinite series, Series with positive and negative terms, The theory of limits, Power series, Maclaurin series, The error term, Taylor series and L'Hopital's rule, Homogeneous differential equations, Linear differential equations, Approximate methods, Review exercise, Answers, Index Discrete mathematics: Introduction, Integers, Linear diophantine equations, Modular arithmetic, Congruences, Integers in different bases, Graphs, Isomorphic graphs, Minimum spanning trees, The shortest path, The Chinese postman, The travelling salesperson problem, Review exercise, Answers, Index
