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Defining injections, surjections, bijections, equivalence relations, and partial orders. 2. Combinatorics (The Art of Counting)
For the advanced student, Biggs delves into groups, rings, and fields. While often considered "pure math," these concepts are increasingly vital in modern cryptography and coding theory. norman l. biggs discrete mathematics pdf
| Chapter | Topic | Key skills | |---------|-------|-------------| | 9 | Recurrence relations | Fibonacci, linear recurrences, characteristic equation | | 10 | Generating functions | Ordinary generating functions, solving recurrences | | 11 | Inclusion–exclusion | Derangements, surjections, Euler’s totient (brief) | While often considered "pure math," these concepts are
Error-correcting codes, linear codes, and perfect codes. He covers Eulerian and Hamiltonian paths, planar graphs,
Most readers agree: Biggs’ treatment of graph theory is worth the price of admission alone. He covers Eulerian and Hamiltonian paths, planar graphs, and graph coloring (including the famous four-color theorem). For computer science students, the sections on trees (spanning trees, rooted trees, binary search trees) are directly applicable to data structures.
You can borrow digital copies of earlier editions through the Internet Archive Significant portions of the text can be previewed on Google Books Student Solutions: Oxford's Companion Website
Advanced tools for solving recurrence relations. 4. Graph Theory and Trees