## CS 310-0 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Miguel A. Lerma - Winter 2004

Section 20

MWF 9:00 am - TECH A110

T 9:00 am - TECH A110

`http://www.math.northwestern.edu/~mlerma/courses/cs310-04w/`

This is the web page for CS 310, Winter 2004.
Consult it often for announcements, homework assignments and possible changes to the syllabus.

## Announcements

• There is no TA session on Tuesday March 9th. Pin Ren will extend his Thursday's office hours in the final week to 5pm in order to help you with questions regarding the final exam.

• Final Exam: Friday, March 19, 2004, 9:00-11:00am in TECH A110. It is a cumulative exam, it covers the whole syllabus.
It will be an open notes exam.

## Course Description

725-310-0 Mathematical Foundations of Computer Science

Fundamental concepts and tools in discreet mathematics with emphasis on their applications to computer science. Topics include logic and Boolean circuits; sets, functions, relations, databases, and finite automata: deterministic algorithms, randomized algorithms, and analysis techniques based on counting methods and recurrence equations; trees and more general graphs. Prerequisites: 725-110 or 725-111 and 435-214-3. Prerequisite for: 725-322, 725-332, 725-339, 725-343, 725-351.

#### Learning Goals

At the end of the course, the student should be able to formulate logic expressions for a variety of applications; convert a logic expression into a Boolean circuit, and vice versa; design relational databases; design finite automata to recognize string patterns; apply, adapt, and design elementary deterministic and randomized algorithms to solve computational problems; analyze the running time of non-recursive algorithms with loops by means of counting; analyze the running time of divide-and-conquer recursive algorithms by means of recurrence equations; and use trees and graphs to formulate computational problems.

## Teachers

Instructor Teaching Assistant
Name Miguel A. Lerma Pin Ren
Office Lunt 203 Computer Science Dept. Room 230
1890 Maple Ave.
Phone 1-8020 1-3296
E-mail mlerma at math dot northwestern dot edu p-ren@cs.northwestern.edu
Office Hours by appointment
in Lunt 203
TH 1:30-3:30pm
TH 1:30-5:00pm during final week
in CS Dept. Room 230, 1890 Maple Ave.
Teaching in TECH A110 TECH A110
Code N.A. 223

## Class Logistics

• Textbooks

Richard Johnsonbaugh: Discrete Mathematics, Fifth Edition, 2001, Prentice Hall.

Miguel A. Lerma: Notes on Discrete Mathematics. (See bellow.)

• Problem Sessions

The problem sessions will be held on Tuesdays under the TA's supervision.

• Homework

The homework assignments will be posted on this web page.

• Exams

There will be one one-hour Midterm Exam and one two-hour Final Exam.

• Midterm: Tuesday, February 10, 2004, 9:00-9:50am in TECH A110.
• Final: Friday, March 19, 2004, 9:0-11:00am in TECH A110.

No make-up exams will be given. In the event of an extreme and well documented absence (such as hospitalization) the final may be weighted to count for the missing exam. In the case of a missed exam, contact the instructor as soon as possible.

The course will be graded as follows:

• Homework Assignments: 30%
• Midterm: 30%
• Final: 40%

The lowest homework score will be dropped in calculating the homework grade.

If you want to change sections, or add/drop the course, please do so at the CS Department Office.

## Lectures and Homework Assignments

Note: I am going to be releasing notes ("Notes on Discrete Mathematics", in PDF format) that you can download by clicking in the links of the "subject" column of the syllabus bellow. The introduccion is in here:

Depending on various circumstances, the schedule shown bellow may experiment small modifications.

The "sections" listed on the 4th column are from Johnsonbaugh's book.

The "Suggested Exercises" column contains some exercises from the book that you may find useful to try. They are not homework nor need to be turned in.

Lect. Date Subject Sections Suggested Exercises Homework
Assignments
Logic and Proofs
1 Mon 1/5 Propositions 1.1-1.2 1.1: 20-24, 27-29, 41-46;
1.2: 28-31, 38-39, 43-46
2 Wed 1/7 Quantifiers, Proofs 1.3-1.4 1.3: 17-35; 1.4: 21-25, 32-36
3 Fri 1/9 Mathematical Induction 1.6 1.6: 2-7, 19, 22, 23, 26, 46 set 1 - Due Tue 1/20/2004
The Language of Mathematics
4 Mon 1/12 Sets 2.1 2.1: 1-10, 25-29, 31, 33, 35, 78, 82
Probl. Tue 1/13
5 Wed 1/14 Sequences, Strings 2.2 2.2: 4, 6, 8, 10, 43, 45, 74, 82, 88-92, 96-100
6 Fri 1/16 Relations 2.4-2.6 2.4: 19-24, 29-34; 2.5: 9-14, 30-31; 2.6: 1-6 set 2 - Due Tue 1/27/2004
7 Mon 1/19 Functions 2.8 2.8: 10-15, 19-23, 26-27, 36-37, 56, 78-84
Probl. Tue 1/20
Algorithms
8 Wed 1/21 Algorithms, Recursiveness, Complexity 3.1-3.2,3.4-3.5 3.2: 19-21; 3.4: 8-9, 12-13, 27-28; 3.5: 1-12, 16-25
9 Fri 1/23 The Euclidean Algorithm 3.3 3.3: 1-5, 21-24 set 3 - Due Tue 2/3/2004
10 Mon 1/26 Modular Arithmetic,
The RSA Public-Key Cryptosystem
3.7 3.7: 1-9
Probl. Tue 1/27
Counting
11 Wed 1/28 Combinatorics 4.1-4.2 4.1: 5, 17-20, 28-30, 34-37, 42-46, 60, 62; 4.2: 10-14, 25-29, 31-34, 58-62
12 Fri 1/30 More Combinatorics,
Pigeonhole Principle
4.6-4.8 4.6: 1-3, 7-9, 15-17, 22-24; 4.7: 1, 3-5, 10-11; 4.8: 1-10 set 4 - Due Tue 2/10/2004
13 Mon 2/2 Probability 4.4-4.5 4.4: 11-17, 30-33, 4.5: 1-5, 22-26, 42-45
Probl. Tue 2/3
Recurrence Relations
14 Wed 2/4 Recurrence Relations 5.1-5.2 5.1: 4-8, 37-40, 18-20; 5.2: 14-15, 34-36
Graph Theory
15 Fri 2/6 Graphs 6.1 6.1: 5-10, 17-18, 22, 27-28, 46-48
16 Mon 2/9 Paths and Cycles 6.2-6.3 6.2: 20-21, 28-38, 6.3: 6-15, 25-36
Exam Tue 2/10 MIDTERM EXAM
up to 5.2
17 Wed 2/11 Representations of Graphs 6.4-6.6 6.4: 1-7; 6.5: 1-3, 7-9, 13-14, 24-25; 6.6: 1-7
18 Fri 2/13 Planar Graphs 6.7 6.7: 6-9, 18-24 set 5 - Due Tue 2/24/2004
Trees
19 Mon 2/16 Trees 7.1-7.2 7.1: 1-4, 24-25,28; 7.2: 22-26
Probl. Tue 2/17
20 Wed 2/18 Spanning Trees 7.3-7.4 7.3: 2,5,7-9; 7.4: 1-5, 21
21 Fri 2/20 Binary Trees 7.5-7.6 7.5: 1,5-8; 7.6: 1-3,6-8,11-15,16-17 set 6 - Due Tue 3/2/2004
22 Mon 2/23 Decision Trees, Tree Isomorphisms 7.7-7.8 7.7: 1-4,9; 7.8: 1-3, 7-12
Probl. Tue 2/24
Boolean Algebras
23 Wed 2/25 Combinatorial Circuits,
Boolean Algebras
9.1-9.3 9.1: 1-3, 22-27, 30-32' 9.2: 1-3, 6-8, 18-19, 21-22; 9.3: 2-5
24 Fri 2/27 Boolean Functions 9.4-9.5 9.4: 1-3, 11-13; 9.5: 1-11 set 7 - Not Due
Automata, Grammars and Languages
25 Mon 3/1 Automata 10.1-10.2 10.1: 1-3, 6-8, 11-13, 21-23; 10.2: 1-6, 13-15, 21-31
Probl. Tue 3/2
26 Wed 3/3 Languages and Grammars 10.3 10.3: 1-3, 7-10, 15-17, 25-27
27 Fri 3/5 Regular Languages 10.4-10.5 10.4: 1-3, 11-13, 21-23; 10.5: 2-4, 7-9
28 Mon 3/8 Review for the Final Exam
29 Wed 3/10 Review for the Final Exam
30 Fri 3/12 Review for the Final Exam
Exam Fri 3/19 FINAL EXAM