Master Discrete Math 2020: More Than 5 Complete Courses In 1

Master Discrete Math 2020: More Than 5 Complete Courses In 1

What you’ll learn

• Analyze and interpret the truth value of statements by identifying logical connectives, quantification and the truth value of each atomic component
• Distinguish between various set theory notations and apply set theory concepts to construct new sets from old ones
• Interpret functions from the perspective of set theory and differentiate between injective, surjective and bijective functions
• Construct new relations, including equivalence relations and partial orderings
• Apply the additive and multiplicative principles to count disorganized sets effectively and efficiently
• Synthesize counting techniques developed from counting bit strings, lattice paths and binomial coefficients
• Formulate counting techniques to approach complex counting problems using both permutations and combinations
• Prove certain formulas are true using special combinatorial proofs and complex counting techniques involving stars and bars
• Connect between complex counting problems and counting functions with certain properties
• Develop recurrence relations and closed formulas for various sequences
• Explain various relationships and properties involving arithmetic and geometric sequences
• Solve many recurrence relations using polynomial fitting
• Utilize the characteristic polynomial to solve challenging recurrence relations
• Master mathematical induction and strong induction to prove sophisticated statements involving natural numbers by working through dozens of examples
• Use truth tables and Boolean Algebra to determine the truth value of complex molecular statements
• Apply various proving techniques, including direct proofs, proof by contrapositive and proof by contradiction to prove various mathematical statements
• Analyze various graphs using new definitions from graph theory
• Discover many various properties and algorithms involving trees in graph theory
• Determine various properties of planar graphs using Euler’s Formula
• Categorize different types of graphs based on various coloring schemes
• Create various properties of Euler paths and circuits and Hamiltonian paths and cycles
• Apply concepts from graph theory, including properties of bipartite graphs and matching problems
• Use generating functions to easily solve extremely sophisticated recurrence relations
• Develop a deep understanding of number theory which involve patterns in the natural numbers