This course provides introduction to applications of discrete mathematical systems. It requires minimal mathematical sophistication. The core topics covered in this course are:

• Logic: propositions, proofs using propositional equivalences.
• Predicates, quantifiers, sets and set operations: union, intersection, difference
• Functions and relations, sequences and summations.
• Modular arithmetic, mathematical induction.
• Mathematical induction, recursive definitions.
• Counting arguments, pigeonhole principle, permutations and combinations.
• Discrete probability, generalized permutations and combination
• Introduction to solving recurrence relations, n-ary relations.
• Boolean algebra.

Examples are drawn from computer science and computer engineering.

Prerequisites: Eligibility to enroll in Mathematics 19A (completion of Mathematics 2B or 3 or Mathematics Placement Exam score of 40 or higher) or completion of Mathematics 19A or 11A.

The following grading system takes into account class participation, exams, homeworks, and reqwards extra effort inside and outside the classroom:

• Homeworks and take-home projects (20%): Weekly homeworks and take-home tests assigned together with some homeworks.
• Midterm 1 (20%) closed book
• Midterm 2 (20%) closed book
• Final Exam (40%) closed book

Midterms and final will be closed book, closed notes.

There are no curves in this class. Your effort determines your grade.

The grading scale for the class will be approximately: A+ (96%-100%), A (92%-96%), A- (88%-92%), B+ (84%-88%), B (80%-84%), B- (77%-80%), C+ (74%-77%), C (64%-74%), D (60%-64%), F (below 60%). I will use my discretion to deal with borderline cases.

Students enrolled in this class are agreeing to the following:

• Work turned in for quizes, exams, and extra-point projects must be the result of individual effort. Homeworks can be solved in teams, but each student is responsible for submitting a homework report.
• Attendance to my lectures is not mandatory.
  By popular demand, attendance to at least one of the discusion sessions is not mandatory. Each student can attend as many of these sections as she or he wants.
• If any work claimed by a student to be his/her own is found to be shared with other students, that will be considered a violation of academic integrity and will be handled accordingly. Students are responsible for grading fairly based on the instructions given by the TAs.
• Students are also responsible for checking the class web page frequently for updates, schedule changes, etc.

In this course we encourage students to get involved in discussions about the class material in- and outside class. However, all work submitted for the class is to be understood by each student. It is fine to solve homework problems as a group, provided that each group member understands the answers she/he submits.

Students should be familiar with the University Academic Intergity Policies, violations of which will not be tolerated. Students who violate University standards of academic integrity are subject to disciplinary sanctions, including failure in the course accompanied by a report which will be part of the student's file, and suspension from the University.

If you have questions or doubts about the UCSC Academic Integrity policies, please see the instructor or the TA.

Our textbook is:
K.H. Rosen, Discrete Mathematics and Its Applications, Sixth Edition, McGraw-Hill, 2007.
ISBN-13 978-0-07-288008-3

We will follow the textbook very closely. We use the Sixth Edition, because it puts more emphasis on proofs.

• Sept 27: Introduction, basic structures
  
• Oct 2: Algorithms, foundations of logic
  (Appendix A-3, Sec. 1.1, 1.2)
• Oct 4: Predicates and quantifiers, sets
  (Sec. 1.3, Sec. 2.1)
• Oct 9: Basic structures (sets), predicates and quantifiers
  (Sec. 2.2, 1.3)
• Oct 11: Nested quantifiers, basic structures (functions), Boolean Algebras
  (Sec. 1.4, 2.3, 11.1)
• Oct 16: Boolean Algebra
  (Sec. 11.2, 11.3, 11.4)
• Oct 18: Boolean Algebra and rules of inference
  (Sec. 11.4, 1.5)
• Oct 23: Rules of inference and proofs
  (Sec. 1.5, 1.6, 1.7)
• Oct 25: MIDTERM 1
• Oct 30: Mathematical proof
  (Sec. 1.7, 2.2, 2.3, 2.4)
• Nov 1: Integers, division and primes
  (Sec. 2.4, 3.4, 3.5)
• Nov 6: More proof
  (Sec. 2.4, 3.4, 3.5)
• Nov 8: Mathematical induction
  (Sec. 4.1)
• Nov 13: Strong induction, applications of induction
  (4.2, 4.3)
• Nov 15: Counting
  (Sec. 5.1, 5.2, 5.3, 5.4)
• Nov 20: MIDTERM 2: It will cover up to strong induction
• Nov 22: HOLIDAY
• Nov 27: More counting
  (Sec. 5.4)
• Nov 29: Probability [cancelled]
  (Sec. 6.1, 6.2)
• Dec 4: Probability
  (Sec. 6.1, 6.2)
• Dec 5: Probablity, generalized permutations and combinations
  (Sec. 6.2, 5.5)
• Dec 6: Recurrence relations
  (Sec. 7.1, 7.2)
• Dec 11: FINAL EXAM (7:30-10:30PM)

• Sample questions for tests
  You are responsible for going over all class material, even if you do not attend class (you can always ask classmates what was covered).
  
• Any notes complementing the textbook would be posted here.