In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?
Tag: Set Theory
Lecture 16: Counting Rules I
What Does It Mean to Be a Number? (The Peano Axioms)
If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?
Crisis in the Foundation of Mathematics
What if the foundation that all of mathematics is built upon isn’t as firm as we thought it was?
Note: The natural numbers sometimes include zero and sometimes don’t — it depends on how you define it. Within logic, zero is always included as a natural number.
A Computational Introduction to Number Theory and Algebra
The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications.
Applied Discrete Structures
This textbook contains the content of a two semester course in discrete structures, which is typically a second-year course for students in computer science or mathematics, but it does not have a calculus prerequisite. The material for the first semester is in chapters 1-10 and includes logic, set theory, functions, relations, recursion, graphs, trees, and elementary combinatorics. The second semester material in chapters 11-16 deals with algebraic structures: binary operations, groups, matrix algebra, Boolean algebra, monoids and automata, rings and fields.
Linear Algebra
Linear Algebra is a text for a first US undergraduate Linear Algebra course. You can use it as a main text, as a supplement, or for independent study. It is Free. The book, the complete answers to all exercises, classroom presentation slides, and a lab manual using Sage, are all available for download, as well as for purchase. The third edition incorporates many suggestions sent by users, including many more beginning exercises, and a new Topic on coupled oscillators and eigenvalues.