Course Overview:
The course is to introduce students to the techniques that may be used and enhanced later in professions related to Computer Science. Computer Science specialists could choose a career of developer, analyst, manager, etc. It is important for all of them to understand or to create formal (most often mathematical) description of the problem to be solved. This course covers a wide range of different aspects of discrete mathematics that are applicable to solving programming problems: proofs by induction; mathematical reasoning, propositions, predicates and quantifiers; sets; relations, graphs, and trees; functions; counting, permutations and combinations.

Prerequisites:
Students should have a fundamental understanding of mathematical reasoning as well as be competent in solving applied algebra problems. The most important prerequisites are interest in the subject, willingness to dedicate necessary resources in terms of time and intellectual effort, and willingness to actively participate in the learning process. No programming skills are required to pass the course.  

Text Books:
Kenneth Rosen, “ Discrete Mathematics and Its Applications”, 7-th Edition, Mc Graw Hill, 2012. 

Grading:
The students will be graded based on course/discussion participation (10%), homework assignments (40%), two midterm exams (20%), one final exam (30%). 
Final grade: A(>=92), A-(>=90), B+(>=87), B(>=82), B-(>=80), C+(>=77), C(>=72), C-(>=70), D+(>=67), D(>=62), D-(>=60) and F (<60).  

Late submission policy:
Exponential penalty -- late for one day loses half, two day loses another half of the remaining, and so on and so forth. 

Topics:

• Introduction to Discrete Structures.
• Logic Inference, Predicates, Qualifiers.
• Boolean Algebra, Logic Gates, Logic Minimization.
• Sets, Functions, Sequences, Sums, Matrices, Matrix Algebra.
• Algorithms, Searching, Sorting, Complexity of Algorithms.
• Number Theory, Cryptography, Modular Arithmetic.
• Induction and Recursion.
• Counting.
• Relations.
• Graphs.
• Trees.

Course schedule:

Class	Date	Topic	Reading	Homework	Slides
1	8/27/2018	Introduction			Lecture_1
2	8/29/2018	Propositional Logic	Ch 1.1-1.2		Lecture_2
3	8/31/2018	Predicate Calculus and Quantifiers	Ch 1.3-1.4		Lecture_3
	9/3/2018	Class Suspended -- Labor Day
4	9/5/2018	Quantifiers and Rules of Reference	Ch 1.4-1.5		Lecture_4
5	9/7/2018	Proofs	Ch 1.5-1.8	Homework 1 Assigned.	Lecture_5
	9/10/2018	Class Suspended -- Rosh Hashanah
6	9/12/2018	Introduction to Sets	Ch 2.1		Lecture_6
7	9/14/2018	Set Operations and Introduction to Functions	Ch 2.2-2.3		Lecture_7
8	9/17/2018	Functions	Ch 2.3	Homework 1 Due.	Lecture_8
	9/19/2018	Class Suspended -- Yom Kippur
9	9/21/2019	Sequences and Summation (1)	Ch 2.4		Lecture_9
10	9/24/2019	Sequences and Summation (2)	Ch 2.4		Lecture_10
11	9/26/2018	Cardinality of Sets	Ch 2.5		Lecture_11
12	9/28/2018	Matrices	Ch 2.6	Homework 2 Assigned	Lecture_12
13	10/1/2018	Algorithms	Ch 3.1		Lecture_13
14	10/3/2018	Growth of Functions and Complexity	Ch 3.2-3.3		Lecture_14
15	10/5/2018	Integers and Division	Ch 4.1		Lecture_15
16	10/8/2018	Midterm Exam 1	Ch 1.1-1.8, Ch 2.1-2.6	Homework 2 Due and Midterm Exam 1
17	10/10/2018	Modular Arithmetic	Ch 4.1		Lecture_16
18	10/12/2018	Integer Representations	Ch 4.2		Lecture_17
19	10/15/2018	Primes and Greatest Common Divisors	Ch 4.3		Lecture_18
20	10/17/2018	Cryptograph	Ch 4.6		Lecture_19
21	10/19/2018	Cover Midterm Exam 1 and Homework
22	10/22/2018	Mathematical Induction	Ch 5.1-5.2	Homework 3 Assigned	Lecture_20
23	10/24/2018	Strong Induction and Well-Ordering	Ch 5.2		Lecture_21
24	10/26/2018	Structural Recursion and Induction	Ch 5.3		Lecture_22
25	10/29/2018	Recursive Algorithms	Ch 5.4		Lecture_23
26	10/31/2018	Recursive Algorithms and Basic Counting Rules	Ch 5.4 and Ch 6.1		Lecture_24
27	11/2/2018	Pigeonhole Principle, Permutations and Combination	Ch 6.2-6.3	Homework 3 Due	Lecture_25
28	11/5/2018	Binomial Coefficients and Identities	Ch 6.4	Homework 4 Assigned	Lecture_26
29	11/7/2018	Inclusion-exclusion Principle	Ch 6.4		Lecture_27
30	11/9/2018	Discrete Probability	Ch 7.1-7.2		Lecture_28
31	11/12/2018	Conditional Probability	Ch 7.2-7.3		Lecture_29
32	11/14/2018	Midterm Exam 2	Ch 3.1 - Ch 6.4	Homework 4 Due and Midterm Exam 2
33	11/16/2018	No class
34	11/19/2018	Bayes Rules, Expected Value, Variance and Binorminal Distribution	Ch 7.3-7.4		Lecture_30
	11/21/2018	Class Suspended -- Thanksgiving Break
	11/23/2018	Class Suspended -- Thanksgiving Break
35	11/26/2018	Relations (1)	Ch 9.1-9.3		Lecture_31
36	11/28/2018	Relations (2)	Ch 9.4-9.5	Homework 5 Assigned	Lecture_32
37	11/30/2018	Graph Theory (1)	Ch 10.1-10.5		Lecture_33
38	12/3/2018	Graph Theory (2)	Ch 10.1-10.5		Lecture_34
39	12/5/2018	Trees	Ch 11.1-11.5		Lecture_35
40	12/7/2018	Recap and Review (1)		Homework 5 Due
41	12/10/2018	Recap and Review (2)
42	12/17/2018	Final Exam	Ch 1-Ch 11	Final Exam