Lecture Titles
0 Introduction
Chapter 1 Whole Numbers
1.1 Introduction to Whole Numbers
1.2 Addition of Whole Numbers
1.3 Subtraction of Whole Numbers
1.4 Multiplication of Whole Numbers
1.5 Division of Whole Numbers
1.6 Exponential Notation and the Order of Operations Agreement
1.7 Prime Numbers and Factoring

Contents: Basic Concepts of Logic; Truth-Functional Connectives; Validity in Sentential Logic; Translations in Sentential Logic; Derivations in Sentential Logic; Translations in Monadic Predicate Logic; Translations in Polyadic Predicate Logic; Derivations in Predicate Logic.

The series of expository lectures intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory, residue index theorem of Connes and Moscovici, etc.

W. W. Norton & Company | 579 pages | PDF | 42 MB

Russell's classic 'The Principles of Mathematics' sets forth his landmark thesis that mathematics and logic are identical -- that what is commonly called mathematics is simply later deductions from logical premises. His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

Ready to exercise those brain cells? Humans have been having fun with mathematics for thousands of years. Along the way, they've discovered the amazing utility of this field—in science, engineering, finance, games of chance, and many other aspects of life. This course of 24 half-hour lectures celebrates the sheer joy of mathematics, taught by a mathematician who is literally a magician with numbers. Professor Arthur T. Benjamin of Harvey Mudd College is renowned for his feats of mental calculation performed before audiences at schools, theaters, museums, conferences, and other venues.

Mathematics from the Visual World, taught by veteran Teaching Company Professor Michael Starbird of The University of Texas at Austin, takes Plato's dictum to heart and introduces you to the terms, concepts, and astonishing power of geometry. In 24 richly illustrated lectures, you learn that geometry is everywhere. It is the key to scientific disciplines from cosmology to chemistry. It is central to art and architecture. It provides deep insights into algebra, calculus, and other mathematical fields. And it is stunning to contemplate in its beauty.

These video lectures of Professor Gilbert Strang teaching 18.06 were recorded live in the Fall. Support for the video production was provided by the Lord Foundation of Massachusetts under a grant to the MIT Center for Advanced Educational Services.

01 The Geometry of Linear Equations.rm
02 Elimination with Matrices.rm
03 Multiplication and Inverse Matrices.rm
04 Factorization into A = LU.rm
05 Transposes, Permutations, Spaces R^n.rm
06 Column Space and Nullspace.rm
07 Solving Ax = 0 - Pivot Variables, Special Solutions.rm
08 Solving Ax = b - Row Reduced Form R.rm
09 Independence, Basis, and Dimension.rm
10 The Four Fundamental Subspaces.rm

This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization.