## Discrete Mathematics

A discrete mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this text stresses mathematical reasoning and the different ways problems are solved. Five important themes are interwoven in this text: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling.

Discrete Math helps provide…

• the machinery necessary for creating sophisticated algorithms
• the tools for analyzing their efficiency
• the means of proving their validity

We all know that math is the most rigorous of the scientific disciplines in the sense that its results are acknowledged to be true while in other disciplines, the truth of the conclusions depends on the how accurate the underpinning physical assumptions were. In reality, this is over-optimistic. Just as in physics you have to start somewhere abstract and outside of physics, so it must be with mathematics. In physics space and time are mathematical abstractions assumed to be our physical world. In math you start with some intuitive concepts which our brain developed to help us succeed in the world, concepts which cannot be explained, concepts that just are but that are intuitively obvious.

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 Course Outline Discrete mathematics and its applications 6th Edition(1-7) Discrete mathematics and its applications 6th Edition(8-12) Lecture 1:  Introduction to the course, Propositional Logic, Logical Operators, Conditional Statements, Biconditional Statements Lecture 2: Converse, Contrapositive and Inverse, Translating English Sentences, Logic Puzzles Lecture 3: Propositional Equivalences, Predicates & Quantifiers, Negating Quantified Statements Lecture 4: Nested Quantifiers, Order of Quantifiers, Negating Nested Quantifiers Lecture 5: Rules of Inference, Building Argument, Fallacies, Introduction to Proofs Quiz 1 Solution Lecture 6: Direct Proofs, Proofs by Contraposition, Proofs by Contradiction Lecture 7: Mistakes in Proofs, Proof Methods and Strategy Lecture 8: Sets, Subsets, Power Sets, Set Operations and Identities, Computer Representation of Sets Lecture 9: Functions, One-to-One and On-to Functions, Inverse Functions, Compositions of Functions Lecture 10: Sequences and Summations, Countable and Uncountable Sets Lecture 11: Introduction to Algorithms, Linear Search, Binary Search Lecture 12: Sorting, Bubble Sort, Insertion Sort, Greedy Algorithms