MA 2025 (4-1) Logic and Discrete Mathematics I

MA 2025 (4-1) Logic and Discrete Mathematics I Summer 2012

Instructor : Prof. Ralucca Gera Office : 260 Spanagel Phone : (831) 656-2230; Fax : (831) 656-2355 E-mail : [email protected] Web-site : http://faculty.nps.edu/rgera/MA2025/Winter2011/home.html

Office Hours : Tue, Wed, Thu 10-11am, (or by appointment), in 260 Spanagel. Textbook : Discrete Mathematics and Its Applications, 7th Edition, K.H. Rosen, WCB/McGraw-Hill 2012. Homework: Regular homework assignments will be made but none will be collected. Homework will be posted on line. Make-up policy : There will be absolutely no accepting of late or make-up assignments. If you know you will be missing school, you can take the quiz ahead of time, if you let me know two days before the quiz will be given. If you cannot attend the Exams, a makeup will be given only if you have informed me of your expected absence no later than 2 class periods preceding the test. For sudden illness and accidents, please see me upon your return to class. Grading: Your final grade is the average of your 4 exams (100 points each).

Course Description: MA 2025 is the first course in a two-course sequence designed to provide a foundation in logic and elementary discrete mathematics. The course is useful for students from a number of disciplines, but has been specifically tailored for students of computer science. The principal emphasis is on logic and its application to mathematical proof. Once the logical underpinnings are firmly in place, the course applies them to a handful of fundamental areas of discrete mathematics that are also essential in computer science. These are naive set theory, properties of functions (and a menagerie of especially useful functions), integer divisibility, mathematical induction, and elementary combinatorics. Three of these areas (elementary number theory, mathematical induction, and combinatorics) are pursued in greater depth in the follow-on course, MA3025.

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Week Sections

Topics

1: 2: 3: 4: Exam

Propositional Logic and Applications of Propositional Logic Propositional Equivalence, Quantifiers Nested Quantifiers, Rules of Inference Methods of Proof and Strategy

1.1, 1.3, 1.5, 1.7, 1

1.2 1.4 1.6 1.8

5: 2.1, 2.2 Sets and Set Operations 6: 2.3, App. A2 Functions: Definitions, Properties, Composition. Exponential and Log functions Exam 2 7: 8: 9: Exam

4.1, 4.2 2.4 5.1 3

10: 6.1, 6.2 11: 6.3 Exam 4

Integer Division, Primes, and the GCD, Euclidean Algorithm Sequences and Summation, Methods of Proof (Induction) Fundamentals of Counting, The Pigeonhole Principle Permutations and Combinations

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