Nassimi, David

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New Jersey Institute of TechnologyDigital Commons @ NJITComputer Science Syllabi NJIT SyllabiFall 2019CS 506-851: Foundations of Computer Science IDavid NassimiFollow this and additional works at: https://digitalcommons.njit.edu/cs-syllabiThis Syllabus is brought to you for free and open access by the NJIT Syllabi at Digital Commons @ NJIT. It has been accepted for inclusion inComputer Science Syllabi by an authorized administrator of Digital Commons @ NJIT. For more information, please contactdigitalcommons@njit.edu.Recommended CitationNassimi, David, "CS 506-851: Foundations of Computer Science I" (2019). Computer Science Syllabi. 30.https://digitalcommons.njit.edu/cs-syllabi/30 1 CS 506, Online Course Syllabus  Foundations of Computer Science I (Discrete Mathematics for CS) Dr. David Nassimi Fall 2019  Prof. David Nassimi Website Moodle Webex web.njit.edu/~nassimi/cs506   moodle.njit.edu njit.webex.com Email: Nassimi@njit.edu Office Hours TA: Webex Live Sessions Thurs 7-8 pm  TBA  Course Description:  This is a graduate bridge course that provides the mathematical and analytical foundations of computer science.  It is designed for entering MS students who need to strengthen their math background before taking the core course on algorithms (CS 610).  This course carries credits towards MS degree.  The course covers the material traditionally known as “discrete mathematics”, with special emphasis on CS applications and analysis of algorithms.  The course topics include sets and logic, proof techniques, proof  by induction, functions, relations, analysis of algorithms, recursion, recurrence equations, divide-and-conquer technique, counting methods, permutations and combinations, basic discrete probability, and an introduction to number theory.   (Future plans are to also incorporate an introduction to graphs and trees. )  The course currently has 10 Homework Assignments (on paper exercises), and 2 Programming Assignments to be implemented and run on a computer.   Text:   R. Johnsonbaugh, Discrete Mathematics, 7th Edition, Pearson Prentice Hall, 2009.   ISBN-13:  978-0-13-159318-3;     ISBN-10:   0-13-159318-8  Course Objectives (what you are expected to know to complete this course) 1. Know basic mathematical tools and terminologies used in computer science  2. Know set algebra, propositional logic, reasoning, and basic proof techniques 3. Know induction, recursion, recurrence equations, and how they are interrelated 4. Know the mathematical tools used to analyze efficiency of algorithms 5. Implement simple programs and run experiments to measure their time complexity 6. Learn permutations/combinations, basic discrete probability, and applications 7. Understand basics of number theory  Course Evaluation (Assessment): Evaluation:  Assignments 24% Midterm Exam 38% Final Exam 38% Notes:   Pictured NJIT ID required for all exams.  All exams are on campus, closed books/notes.    Policies: 1. Assignments must be done by you individually.  Team-work not allowed. 2. Submit all assignments on Moodle by the due date. 3. Moodle: You must check the moodle page and your emails regularly for possible announcements.   2 4. Website: Copies of a few old exams are posted on my website.   Academic Integrity:  Familiarize yourself with NJIT Honor Code: http://integrity.njit.edu.  Any evidence of dishonesty will be dealt with seriously and reported to the Dean of Students.  Submission of Assignments: There are two types of assignments (all submitted on moodle):   Homework Assignments (10):  These are problem sets and may be either typed or hand-written neatly and scanned and uploaded in PDF format. If homework asks for an algorithm, it still means pseudocode on paper.  Programming Assignments (2): These assignments must be implemented and run on computer to produce results. Submissions of these assignments must be in multiple files. (Please DO NOT Zip your files into one file, because the TA may have trouble unzipping it.) Multiple files are: 1. Source code of the program.  The TA will need to read this file to evaluate your program, and run the program to verify that it works. (PDF won’t work!) 2. Input data, if relevant 3. Output produced by the program 4. Discussion and Analysis, if relevant   CS 506 Course Outline Week Approx. Topic Reading Course Material  Algebra Self-Review  1-2 Sets and Logic  Sets Propositional Logic  (App:  Google Search) Quantifiers (App:  Database operations)  Module 1  Sets Module 2  Logic 3 Proof Techniques Direct Proof, Counterexample, Contrapositive,  Proof by Contradiction, Enumeration Proof  Proof by Induction;  Strong Induction Module 3  Proofs 4-5 Functions and Relations  Functions Relations Properties: Reflexive, Symmetric, Transitive  Partial Order, Total Order,  Equiv. Relations  Matrices of Relations  Application: Relational Databases  Module 4  Functions Module 5  Relations 6-7 Algorithms Analysis of Algorithms Recursive Algorithms Use of Recurrences to Analyze Algorithms  Module 6 Analysis Alg. Module 7  Recursion 8 Midterm Exam   3 9 Recurrence Equations Divide-and-Conquer Recurrences Master Theorem Linear Recurrences  Module 8  Recurrences  10 Counting Methods Permutations and Combinations Principle of Inclusion/Exclusion Pigeonhole Principle  Module 9  Permutations & Combinations  11 Discrete Probability Module 10  Probability 12-13 Number Theory and Cryptography Module 11 Number Theory 14 Review  16 Final Exam     

CS 506-851: Foundations of Computer Science I

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CS 506-851: Foundations of Computer Science I

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