MATH 2350 Final Exam Study Guide Fall 2016 The final exam will be Wed, Dec 14 from 10:30AM to 12:30PM. The exam will cover topics from the entire semester with an emphasis on those since the second exam. You should be familiar with sections 1.1-1.6, 2.1-2.6, 3.1-3.3, 4.1-4.4, and 7.1-7.2 of the textbook. There will not be any questions about the Josephus game, partitions of a set, duality principle, or minimal spanning trees. In particular, topics will include: Sequences Functions Closed formula Domain Recursive formula Codomain Sigma notation for sums Binary Relations Smullyan's Island Domain Truth tables Codomain Propositions Arrow Diagrams Tautology One-set Contradiction Two-set Negation Inverse Relations Logical Equivalence Inverse Functions Predicates Composition of Functions Negation Composition of Relations Quantifiers Invertible functions Negation Onto and one-to-one functions Counterexamples One-to-one correspondence Implications Set Cardinality Negation Infinite Sets Converse Cantor-Bernstein Theorem Inverse Cantor's Theorem Contrapositive Countable/Uncountable sets Proof Writing Reflexive Tracing proofs Irreflexive Proof by contrapositive Symmetric Divisibility of Integers Antisymmetric Rational Numbers Transitive Proof by Cases Partial Order Division Theorem Hasse diagram mod Total ordering Mathematical Induction Eulerian Trail/Circuit Sums as recursive sequences Graphs Fundamental Theorem of Arithmetic Vertices (nodes) Proof by Contradiction Edges Pigeonhole Principle Loops Binary Representation Multiple edges Conversion to and from decimal Adjacent vertices Sets Walk/Closed Walk Subsets Trail/Circuit Intersection Path/Cycle Union Simple Graph Difference Degree of a vertex Complement Connected graph Venn Diagrams Subgraph Inclusion-Exclusion Principle Connected component Cartesian Product Proofs of graph properties Power Set of a Set Tree Element-wise Proofs Leaves Induction proofs on graphs Spanning Tree