# MA2025 Bridge to Advanced Mathematics

MA2025 is a first course in discrete mathematics for students of mathematics and computer science. Topics include propositional and predicate logic up to the deduction theorem, methods of mathematical proof, naive set theory, properties of functions and relations, mathematical induction, an introduction to divisibility and congruences, an introduction to enumerative combinatorics, and an introduction to graphs and trees. Prerequisites: None.

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### Course Learning Outcomes

Prove established results using the main proof techniques:

·       Direct proof

·       Contraposition

·       Induction

Demonstrate proficiency/competencies and strategies for:

·       Using counting techniques, permutations, and combinations.

·       Explaining and use divisibility and modular arithmetic.

·       Applying various properties of relations and partial orders.

·       Constructing closure of relations.

·       Applying basic principles of counting and combinatorics and differentiating when to apply different rules and combinations thereof.

·       Modeling problems using graph theory, and successfully using established theoretical graph concepts.

Apply the essential concepts and proof methods of combinatorics to be able to:

·       Distinguish between a correct and incorrect argument.

·       Break down a result to analyze its parts and use the proof techniques to complete the proof.

·       Identify if two graphs are isomorphic and prove the claim.

·       Draw connections and identify differences between the different ideas that use tree in graph theory.

·       Contrast the use of the concepts of traversal and spanning trees.