The exhaustive list of topics in Discrete Mathematics in which we provide Help with Homework Assignment and Help with Project is as follows:
- Natural Numbers: Well Ordering Principle, Principle of Mathematical Induction.
- Set Theory: Ordered Sets, Relations, Equivalence Relations and Partitions, Modular Arithmetic.
- Functions: Functions, Composition of Functions, one-one, onto and Inverse of a function.
- Basic Counting Principles: Number of one-one, Permutation, Combinations, Number of onto functions, Partitions and Stirling Numbers of Second kind.
- Advanced Counting: Pigeon-hole Principle, Inclusion-Exclusion Principle, Putting Balls into boxes, Round Table Configurations, Counting using Lattice Paths, Catalan Numbers.
- Group Theory:Groups, Subgroups, Cyclic Groups, Characterisation of Cyclic Groups, Lagrange’s Theorem, Normal Subgroups, Homomorphism and the first Isomorphism theorem of groups, Symmetric Group till definition of Alternating Group.
- Group Action, Orbit Stabilizer Theorem and its applications to Polya’s Counting Principle and Polya’s Inventory Problems.
- Recurrence Relations, Generating Functions, Using generating functions to prove results related to certain binomial coefficients.
- Basic Graph Theory: Graphs, Trees, Characterisation of Trees, Rooted Trees.