CS 2233 Discrete Mathematical Structures (Undergraduate, Spring 2011)

 

Instructor

Dr. Shouhuai Xu

TA

  • See below.

What's New?

  • (4/14) Schedule adjustment.
  • (2/17) A PhD student will proctor the Feb 22 exam. There will be no recitation on Feb 22.

Office

Science Building 4.01.46

Office hour

TR 4:45-5:45PM

When & where

  • Class: TR 3:30-4:45pm; HSS 3.04.26; (course website: http://www.cs.utsa.edu/~shxu/cs2233-spring-2011)
  • Recitation Times:

                2231 001 T 5:30 - 6:20pm SB3.01.04 TA: Tahmina Ahmed (tahminaurmi@yahoo.com)
                2231 002 R 5:30 - 6:20pm SB3.01.04 TA: Chayutra Pailom (casanova26@gmail.com)

Textbook:

        Discrete Mathematics and Its Applications, Sixth Edition by Kenneth H. Rosen

Prerequisites:

        CS 1721, CS 1723, and MAT 1223. Concurrent enrollment in CS 2231 is required.

Course Objective:

        To provide the opportunity to understand and be able to use fundamental concepts in discrete mathematics

Course Content (mostly consistent with the content when the course is taught by other faculty members):

  • Propositional and predicate calculus
  • Basic set theory and functions
  • Mathematical proof
  • Techniques for specifying and analyzing algorithms
  • Basic asymptotic complexity and order notation (big-O)
  • Induction, recursion, and recurrences
  • Introduction to relations, equivalence relations, and order relations
  • Elementary discrete probability and number theory
  • Introduction to graph theory and trees

Grading:

  • 15% Each of two Midterm Exams
  • 30% Homework Assignments (hand in at the beginning of the class on a specified date; work alone)

      calculation: (sum of homework scorers) / #homeworks * 30%

  • 5% Attendance
  • 35% Final Exam (Friday, December 10, 7:30am - 10:00am in regular lecture room)
  • The same grade is assigned for CS 2233 and CS 2231.
  • Bonus/extra credit may be given when appropriate.

Course Policy (consistent with the policy when the course is taught by other faculty members):

No make-up exams will be given, except for university sanctioned, excused absences. If you must miss an exam (for a good reason), it is your responsibility to contact me as far before the exam as possible. In most cases, you must talk to me several weeks before the exam for the absence to be excused. At minimum, you must send the instructor email. If it is my judgement that this message should have come earlier, the grade for that exam will be a zero. If a make-up exam is given, it may be harder than the regular exam. Also, a make-up will not be given if the student has discussed the exam with any student that has already taken the exam.

Unless otherwise stated, all assignments are due at the beginning of class on the due date. Assignments turned in after that time may receive a zero, however you should discuss the matter with the instructor, as homework is more important as a learning opportunity than as a measurement device. Do not miss class to finish an assignment. Turn in what you have for partial credit and discuss with the instructor whether turning in the rest later will be acceptable.

You must write your solutions to the assignments by yourself and without help from anyone. You may, however, discuss problems with other students, once you have studied the problem on your own. Do not make it harder for yourself to learn the material by failing to think about problems on your own before you discuss them with others. This will make a big difference to your performance on exams when it really counts.

Advice for Success:

For many students, this course will resemble learning a foreign language in the sense that it requires daily practice to master the material. Do your brain a favor. Work with the material a little each day. Then sleep on it so the new ideas get recorded in your long-term memory. The next day, things that seemed complex will seem quite a bit simpler and you'll be ready to take another step. Don't plan to cram for exams in this class. Most people's brains take time and practice to develop proficiency with abstract mathematics. (And this class demands that you operate at a level of abstraction that may be higher than has been required of you in past math classes.)

Online Student Survey:

Online student survey will be administered between 4/4 and 4/15.

Course schedule (tentative, subject to change):

"This Syllabus is provided for informational purposes regarding the anticipated course content and schedule of this course. It is based upon the most recent information available on the date of its issuance and is as accurate and complete as possible. I reserve the right to make any changes I deem necessary and/or appropriate. I will make my best efforts to communicate any changes in the syllabus in a timely manner. Students are responsible for being aware of these changes."

 

Week

Date

Lecture

 1

Jan. 11

(Sections 1.1 & 1.2) Propositional Logic

Recitation covers the relevant odd-numbered questions.

Homework I (part 1): Section 1.1 exercises 2, 4, 6, 8, 10, 14, 20, 22, 28, 62 (5 points each question).

 

Jan. 13

(Sections 1.1 & 1.2) Propositional Logic

Recitation covers the relevant odd-numbered questions.

2

Jan. 18

 

(Sections 1.1 & 1.2) Propositional Logic

Recitation covers the relevant odd-numbered questions.

Homework I (part 2): Section 1.2 exercises 2, 4, 6, 8, 10, 14, 22, 26, 28, 30 (5 points each question).

 

Jan. 20

 

(Sections 1.1 & 1.2) Propositional Logic

Recitation covers the relevant odd-numbered questions.

3

Jan 25

Homework I due in class

(Sections 1.3 & 1.4 & 1.5) Predicate Logic

Recitation covers the relevant odd-numbered questions.

Homework II (part 1): Section 1.3 exercises 6, 8, 10, 14, 16, 24, 26, 28, 42, 48 (5 points each question).

 

Jan. 27

 

(Sections 1.3 & 1.4 & 1.5) Predicate Logic

Recitation covers the relevant odd-numbered questions and/or Homework I.

Homework II (part 2): Section 1.4 exercises 20, 24, 28, 30, 38; Section 1.5 exercises 2, 20, 24, 26, 28 (5 points each question).

 4

Feb. 1

Homework II due in class

(Sections 1.6 & 1.7) Application: Proofs

Recitation covers the relevant odd-numbered questions and/or Homework II.

Homework III: Section 1.6 exercises 14, 18, 20, 26, 28; Section 1.7 exercises 26, Review questions (page 106) 8, 12, 16, and Supplementary exercise (page 108) 32 (10 points each question).

 

Feb. 3

Homework III due in class

(Sections 2.1, 2.2) Sets and Set Operations

Recitation covers the relevant odd-numbered questions.

Homework IV (part 1): Section 2.1 exercises 4, 8, 16, 26, 32, 34, 38; Section 2.2 exercies 4, 16, 18 (10 points each question).

5

Feb. 8

(Sections 2.3) Functions

Recitation covers the relevant odd-numbered questions and/or Homework III.

Homework IV (part 2): Section 2.3 exercises 2, 10, 12, 16, 20, 22, 32, 34, 68; Review question (page 164) 10 (10 points each question).

 

Feb. 10

Homework IV due in class

(Sections 2.4) Sequences and Sums

Recitation covers the relevant odd-numbered questions.

Homework V (part 1): Section 2.4 exercises 4, 8, 10(a)-10(b), 16(a), 20 (10 points each question).

6

Feb. 15

(Sections 2.4) (Un)Countability

Recitation covers the relevant odd-numbered questions and/or Homework IV.

Homework V (part 2): Section 2.4 exercises 32, 34, 36, 40, 42 (10 points each question).

 

Feb. 17

Homework V due in class

Review: Come prepared with questions

Recitation covers the relevant odd-numbered questions and/or Homework V.

7

Feb. 22

Exam I

 

Feb. 24

(Sections 3.1-3.3) Algorithms

Recitation covers the relevant odd-numbered questions and/or Homework V.

Homework VI (part 1): Section 3.1 exercises 4, 6, 8, 16, 18 (10 points each question).

8

Mar. 1

(Sections 3.1-3.3) Algorithms

Recitation covers the relevant odd-numbered questions.

Homework VI (part 2): Section 3.2 exercises 2, 8, 10, 12 (10 points each question).

 

Mar. 3

(Sections 3.1-3.3) Algorithms

Recitation covers the relevant odd-numbered questions.

Homework VI (part 3): Section 3.3 exercise 4 (10 points).

9

Mar. 8

Homework VI due in class

(Sections 3.4-3.7) Arithmetic

Recitation covers the relevant odd-numbered questions.

Homework VII (part 1): Section 3.4 exercises 24; Section 3.5 exercises 4(a)-4(c), 10, 14(a), 34 (10 points each question).

 

Mar. 10

(Sections 3.4-3.7) Arithmetic

Recitation covers the relevant odd-numbered questions and/or Homework VI.

Homework VII (part 2): Section 3.6 exercise 20; Section 3.7 exercise 6, 10, 12, 18 (10 points each question).

 

Mar. 14-19

Spring break 

11

Mar. 22

Homework VII due in class

(Sections 4.1, 4.2) Mathematical Induction and Strong Induction

Recitation covers the relevant odd-numbered questions.

Homework VIII (part 1): Section 4.1 exercises 4, 6, 10, 14, 38, 40 (10 points each question).

 

Mar. 24

(Sections 4.1, 4.2) Mathematical Induction and Strong Induction

Recitation covers the relevant odd-numbered questions and/or Homework VII.

Homework VIII (part 2): Section 4.2 exercises 6, 12, 26, 32 (10 points each question).

12

Mar. 29

Homework VIII due in class

(Sections 4.3 4.4) Recursive Functions

Recitation covers the relevant odd-numbered questions.

Homework IV (part 1): Section 4.3 exercises 2(a)-2(b), 4(a)-4(b), 8(a) & 8(c), 12, 24 (10 points each question).

 

Mar. 31

(Sections 4.3 4.4) Recursive Algorithms

Recitation covers the relevant odd-numbered questions and/or Homework VIII.

Homework IV (part 2): Section 4.4 exercises 8, 10, 16, 20, 22 (10 points each question).

13

Apr. 5

Homework IV due in class

Review: Come prepared with questions

Recitation covers the relevant odd-numbered questions and/or Homework IV.

 

Apr. 7

Exam II

14

Apr. 12

(Sections 6.1, 6.2) Discrete Probability

Recitation covers the relevant odd-numbered questions.

Homework X (part 1): Section 6.1 exercises 2, 6, 22, 24, 26, 36, Section 6.2 exercises 6, 8, 12, 20, 24, 28 (5 points each question).

 

Apr. 14

((Sections 6.2, 6.3) Applications of Discrete Probability

Recitation covers the relevant odd-numbered questions.

Homework X (part 2): Section 6.3 exercises 2, 6, 18, 20, 22 (10 points each question).

15

Apr. 19

 

(( (Sections 6.2, 6.3) Applications of Discrete Probability

Recitation covers the relevant odd-numbered questions.

 

(Sections 8.1-8.3) Relation: Foundation of Database

Recitation covers the relevant odd-numbered questions.

Homework XI (part 1): Section 8.1 exercises 2, 22, 28, 30, 36, Section 8.3 exercises 2, 6, 12, 14, 16 (5 points each question).

 

Apr. 21

Homework X due in class

(Sections 9.1-9.3) Graphs: Foundation of Many Things

Recitation covers the relevant odd-numbered questions and/or Homework X.

Homework XI (part 2): Section 9.1 exercises 12, 18, 24, 28; Section 9.2 exercises 4, 6, 12, 16, 18; Section 9.3 exercises 6 (5 points each question).

16

Apr. 26

 

Review: Come prepared with questions

Recitation covers the relevant odd-numbered questions and/or Homework XI.

 

Apr. 28

Student Study Day

17

May 6

Final Exam (10:30am - 1:00pm)