20182019– Semester II
 Official Syllabus
 Lecture Notes
 Generic Course Objectives
 Classroom Behaviour
 On the use of electronic aparati
 In Praise of Lectures
 UPR Regulations concerning Academic Integrity and Reasonable Accommodation”
Miscellaneous Notes
 Digraph Taxonomy
 Directed Graphs
 Equivalence Relations
 Simple Graphs
 Elementary Combinatorial Formulae
 The Symmetric Difference
 Balls in Boxes
 BinomialMultinomial Theorems
 Multisets
 Partitions
 Inclusion Exclusion Principle
 On the Number of Surjections
 Function Digraphs
 Group Actions
 Orbit Stabilizer Theorem
 Cycle Structure
 Chemical Isomers and Coloring
Homework
 Functions
 Relations
 Dirichlet Principle
 Elementary Combinatorial Exercises
 Balls in Boxes
 Graph Combinatorics
Sample Exams
Syllabus
 Preliminary material
 Digraphs
 permutation digraphs.
 orders and preorders.
 equivalence relations and partitions.
 lattices and boolean algebras.
 Elementary Combinatorics
 the inclusionexclusion principle.
 the pigeonhole principle.
 the binomial and multinomial theorems and their
relationship with colorings.
 Simple Graphs
 Paths and cycles.
 Graph connectivity.
 Trees.
 Bipartite graphs
 Isomorphism and
automorphism of simple graphs.
 Group Theory
 Permutation and symmetry groups.
 The dihedral groups.
 Permutation groups.
 Cyclic groups.
 Morphisms.
 Congruences and quotients.
 Cosets.
 Lagrange’s Theorem.
 Normal subgroups.
 The first isomorphism theorem.
 Cayley’s Theorem.
 Group Actions
 Actions and subactions.
 Coloring type actions.
 The orbitstabilizer theorem.
 Burnsides lemma.
 Polya Theory
 The Polya–Redfield theorem.
 The counting of chemical isomers.
 The double group and counting of isomorphism classes of simple graphs.
 Miscellaneous applications.
Grade
Your grade will be based upon two partial exams and a comprehensive final exam. Extra credit will not be given. The grading scale will be no worse than the following: A: 90100; B: 8089; C: 6579; D: 5564; F: < 55. Copying or other forms of cheating will result in an automatic F for the course. In accord with UPR regulations, persistent lateness or unexcused abscence from class may result in a failing grade and loss of financial support.
Grading Scale
Letter grade ( A, B, C, E or F )
Text

 Balakrishnan, V. K. Combinatorics McGraw Hill, 1995.
Bibliography
 Peter J. Eccles, Introduction to Mathematical Reasoning, Cambridge University Press, 1999.
 Ian Stewart and David Tall, Foundations of Mathematics, Oxford University Press, 1986.
 R. F. Lax, Modern Algebra and Discrete Structures, (paperback) Addison Wesley 1997.
 R. Lidl and G. Pilz, Applied Abstract Algebra, Springer, 1998.
 G. Polya, Combinatorial enumeration of groups, graphs, and chemical compounds, Springer.
 Robert F. Lax, Modern Algebra and Discrete Structures, Harper Collins, 1991.