Mathematics

• Mathematics (general)
• Open Courseware (OCW)
   
  • Mathematics (specialist OCW)

Mathematics - Open Courseware (OCW)

Introduction to Statistical Thought

textbook in statistical thinking with a likelihood emphasis for students with a good knowledge of calculus and the ability to think abstractly, focus on ideas that statisticians care about, likelihood function and likelihood principle are unifying ideas throughout the text

Interactive Real Analysis

online, interactive textbook for real analysis or advanced calculus in one real variable: sets and Relations, Infinity and Induction, Sequences of Numbers, Series of Numbers, Topology, Continuity and Differentiation, Metric Spaces, Historical Tidbits, Java Tool

Abstract Algebra Online

definitions & theorems etc: integers, functions, groups, polynomials, rings, fields, structure of groups, Galois theory, unique factorization, modules, structure of noncommutative rings, ideal theory of commutative rings

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Combinatorial Structures

BIBD's, Automorphisms, Symmetric BIBD's, Difference Sets and Automorphisms, Finite Fields, Hadamard Matrices and Designs, Resolvable BIBD's, Latin Squares, t-Designs, Orthogonal Arrays and Code

Calculus for Beginners and Artists

Numbers, Linear Functions, Quadratics and Derivatives of Functions, Rational Functions, Exponential Functions, Substitution and the Chain Rule, Trigonometric Functions, Inverse Functions, Numerical Differentiation, Review of Functions and Derivatives, Modeling Applications, Applications of Differentiation, Antiderivative, Areas and Volumes of Parallel Sided Figures, Area under Curve, Numerical Integration, Differential Equations, applets, Flash dialogs

Problem Course in Mathematical Logic

supplies definitions, statements of results, and problems, along with some explanations, examples, and hints, Soundness, Completeness, and Compactness Theorems & applications, Computability, Turing machines and recursive functions, Incompleteness, Gödel Incompleteness Theorems

Introduction to Topology

topics fundamental to modern analysis & geometry, topological spaces & continuous functions, connectedness, compactness, separation axioms, function spaces, metrization theorems, embedding theorems & fundamental group: readings

Collaborative Statistics

Sampling and Data, Descriptive Statistics, Probability Topics, Discrete Random Variables, Continuous Random Variables, The Normal Distribution, The Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Chi-Square Distribution, Linear Regression and Correlation, F Distribution and ANOVA

Single Variable Calculus

differentiation and integration of functions of one variable, with applications