Physical Sciences and Mathematics Commons^™

Introduction To Discrete Mathematics: An Oer For Ma-471, Mathieu Sassolas

Open Educational Resources

The first objective of this book is to define and discuss the meaning of truth in mathematics. We explore logics, both propositional and first-order , and the construction of proofs, both formally and human-targeted. Using the proof tools, this book then explores some very fundamental definitions of mathematics through set theory. This theory is then put in practice in several applications. The particular (but quite widespread) case of equivalence and order relations is studied with detail. Then we introduces sequences and proofs by induction, followed by number theory. Finally, a small introduction to combinatorics is …

Third And Fourth Binomial Coefficients, Arthur T. Benjamin, Jacob N. Scott '11

All HMC Faculty Publications and Research

While formulas for the sums of kth binomial coefficients can be shown inductively or algebraically, these proofs give little insight into the combinatorics involved. We prove formulas for the sums of 3rd and 4th binomial coefficients via purely combinatorial arguments.

Solution To Problem 1751, A Combinatorial Identity, Arthur T. Benjamin, Andrew Carman '09

All HMC Faculty Publications and Research

A combinatorial proof to Iliya Bluskov's proposed Problem 1751.

Q.954 And A.954, Quickie Problem And Solution, Arthur T. Benjamin, Michel Bataille

All HMC Faculty Publications and Research

Problem and proof proposed by authors.

Another proof, using lattice paths, can be found in Robert A. Sulanke's article, Objects Counted by the Central Delannoy Numbers, The Journal of Integer Sequences, Vol 6, 2003. A proof by polynomials is in Michel Bataille's paper Some Identities about an Old Combinatorial Sum, The Mathematical Gazette, March 2003, pp. 144-8. A slight change in the above proof leads to m ≥ n, a generalization proved by Li Zhou using lattice paths in The Mathematical Gazette.