Math 3012 - Applied Combinatorics
Course Syllabus
Text: There is no required text for this course. Lecture notes will be distributed on this web site. However, recognizing that some students may want to have supplementary reading materials, you will find the titles and authors of some texts in Applied Combinatorics listed at the bottom of the page, including the one which has been widely used at Georgia Tech.
Outline of Topics:
Discrete Structures: Graphs, digraphs, networks, designs, posets, strings, patterns, distributions, coverings, partitions.
Enumeration: permutations, combinations, inclusion/exclusion; generating functions; recurrence relations, Polya counting.
Algorithms and Optimization: Sorting, spanning trees, shortest paths, eulerian circuits, hamitonian cycles, graph coloring, planarity testing, network flows, bipartite matchings, chain partitions.
Classes meet: Room 1 in Weber SST, Tuesdays and Thursdays, 8:05 - 9:25am. Please be on time and ready to learn.
Grading Scale: Grades will be assigned on the traditional scale:
| A | 90 or higher |
| B | 80 - 89 |
| C | 70 - 79 |
| D | 60 - 69 |
| F | Below 60 |
Grading Policy: Grades will be determined by the following distribution:
|
60% |
Three in semester tests |
|
10% |
Homework, quizzes and projects |
|
30% |
Final Exam |
Tests: There will be thee tests during the term, each counting 20% of the final grade, i.e., altogether, these three tests will count for 60% of the final grade.
Homework, Quizzes and Projects: 10% of the final grade will be determined by homework, quizzes and projects. Some homework problems will be turned in electronically and graded by computer. Other homework problems will be assigned or a regular basis but will not be collected for grading. Students are strongly encouraged to collaborate with other students on homework problems that are not turned in for grading but must do their own work for any problems turned in for credit..
Final Exam: The final exam is (tentatively) set for Thursday, May 4 from 2:50 - 5:40pm. This exam will be cumulative and will count for 30% of the final grade.
Computing element: This course is a math course. But combinatorics is closely related to computer science, and students will be required to use and understand computer programs developed for this course. On the other hand, no prior programming knowledge is assumed.
Attendance: Students are expected to attend all lectures without exception. Make-up exams will be given only for (1) official representation of the Institute, and (2) documented medical emergencies.
Student Support: Professor Trotter and Mitch Keller, the Graduate Teaching Assistant, hold regularly scheduled office hours, and students are strongly encouraged to drop by for help. Come sooner rather than later. Experience shows that some Georgia Tech students are reluctant to ask for help as it something they never had to do in high school. Don't fall into this trap. The School of Mathematics wants every student to succeed and we will help you if you make the effort.
Math Tutor Center: Free tutoring services in the Math Lab, located in Skiles 257. Hours are 11:00am - 5:00pm, Monday through Thursday. Tutoring services are also provided by OMED and the Learning Success Program.
Academic Integrity: Students are reminded of the obligations and expectations associated with the Georgia Tech Academic Honor Code.
Recommended Sources for Supplementary material: Discrete and Combinatorial Mathematics, Fifth Edition, by Ralph P. Grimaldi, published by Addison Wesley, and Computational Applied Mathematics, by Pemmaraju and Skienna. Two other books that you may find helpful are: Applied Combinatorics, by Roberts and Tesman, published by Prentice Hall; and Foundations of Applied Combinatorics, by Bender and Williamson.