- Homework assignment 1 solutions
- Homework assignment 2 solutions
- Homework assignment 3 solutions
- Homework assignment 4 solutions
- Solutions to the midterm practice
- Homework assignment 5 solutions
- Homework assignment 6 solutions
- Homework assignment 7 solutions
- Homework assignment 8 solutions
- Homework assignment 9 solutions
- Homework assignment 10 solutions
- Homework assignment 11 solutions
Course description
The purpose of this course is to understand and use (abstract) discrete structures that are backbones of computer science. In particular, this class is meant to introduce logic, proofs, sets, relations, functions, counting, and probability, with an emphasis on applications in computer science.
Prerequisites:
2 years of high school algebra.
Textbook:
Kenneth Rosen. Discrete Mathematics and Its Applications, 5th Edition , McGraw Hill Publishing Co., 2003. ( link to forth edition)
Tentative Syllabus
- Logic: propositional logic, logical equivalence, predicates & quantifiers, and logical reasoning.
- Sets: basics, set operations
- Functions: one-to-one, onto, inverse, composition, graphs
- Integers: greatest common divisor, Euclidean algorithm.
- Sequences and Summations
- Mathematical reasoning: Proof strategies, Mathematical Induction, Recursive definitions, Structural Induction
- Relations: properties, Combining relations, Closures, Equivalence, partial ordering
- Counting: basic rules, Pigeon hall principle, Permutations and combinations, Binomial coefficients and Pascal triangle.
- Probability: Discrete probability. Expected values and variance.
Lectures
| Lectures | Topic(s) | Assignments | |
|---|---|---|---|
| January 4 |
Administrivia ( Course description)
Readings: Introduction |
. | January 9 |
Propositional logic
Readings: Chapter 1.1. |
January 11 |
Propositional logic. Translations.
Readings: Chapter 1.1, 1.2. |
January 13 |
Propositional logic. Equivalences.
Readings: Chapter 1.1, 1.2. |
Homework assignment 1 | January 18 |
Predicate logic.
Readings: Chapter 1.3. |
January 20 |
Predicate logic. Translation.
Readings: Chapter 1.3. |
Homework assignment 2 | January 23 |
Predicate logic. Translation II.
Readings: Chapter 1.4. |
January 25 |
Methods of proof. Formal proofs using propositional logic.
Readings: Chapter 1.5. |
January 27 |
Methods of proof. Informal proofs.
Readings: Chapter 1.5. |
Homework assignment 3 | January 30 |
Sets
Readings: Chapter 1.6. |
February 1 |
Sets and set operations
Readings: Chapter 1.6., 1.7. |
February 3 |
Sets and set operations
Readings: Chapter 1.6., 1.7. |
Homework assignment 4 | February 6 |
Functions
Readings: Chapter 1.8. |
February 8 |
Functions
Readings: Chapter 1.8. |
February 10 |
Integers, primes
Readings: Chapter 2.4. |
| February 13 |
Midterm review
Readings: Chapter 1. |
February 15 |
Midterm exam
Readings: Chapter 1. |
February 17 |
Integers and division (greatest common divisor, least common multiple)
Readings: Chapter 2.4. and 2.5. |
Homework assignment 5 |
| February 20 |
Congruencies and their application
Readings: Chapter 2.4. |
||
| February 22 |
Sequences. Arithmetic and Geometric progression.
Readings: Chapter 3.2. |
||
| February 24 |
Summations. Arithmetic and Geometric series.
Readings: Chapter 3.2. |
Homework assignment 6 | |
| February 27 |
Summations, countable sets
Readings: Chapter 3.2. |
||
| March 1 |
Inductive proof
Readings: Chapter 3.3. |
Homework assignment 7 | |
| March 13 |
Mathematical induction. Recursion.
Readings: Chapter 3.4.. |
||
| March 15 |
Counting. Basic counting rules.
Readings: Chapter 4.1. |
||
| March 17 |
Counting. Pigeonhole principle.
Readings: Chapter 4.2. |
Homework assignment 8 | |
| March 20 |
Counting. Permutations.
Readings: Chapter 4.3. |
||
| March 22 |
Counting. Combinations. Binomial coefficients.
Readings: Chapter 4.3. and 4.4. |
||
| March 24 |
Counting. Generalized Permutations and Combinations
Readings: Chapter 4.5. |
Homework assignment 9 | |
| March 27 & March 29 |
Midterm exam 2 review
Readings: Chapters 2,3,4 |
||
| March 31 |
Midterm exam 2
Readings: Chapters 2,3,4 |
April 3 |
Probabilities. Intro.
Readings: Chapter 5 |
April 5 |
Probabilities. Conditional probabilities. Independence.
Readings: Chapter 5 |
April 7 |
Probabilities
Readings: Chapter 5 |
Homework assignment 10 | April 10 |
Probabilities. Random variable.
Readings: Chapter 5 |
April 12 |
Probabilities. Expected value
Readings: Chapter 5 |
April 14 |
Relations
Readings: Chapter 7.1. |
Homework assignment 11 | April 17 |
Relations. properties.
Readings: Chapter 7.2. |
April 19 |
Combining Relations.
Readings: Chapter 7.3. |
April 21 |
Relations. Closures
Readings: Chapter 7.4. |
Grading
- Lectures 10 %
- Homework assignments 25%
- Exams 65%
Homeworks
There will be weekly homework assignments. The assignments are due at the beginning of the class on the day specified on the assignment. In general, no extensions will be granted.
Additional Student Resources
Academic Honesty
All the work in this course should be done independently. Collaborations on homeworks are not permitted. Cheating and any other antiintellectual behavior, including giving your work to someone else, will be dealt with severely. If you feel you may have violated the rules speak to us as soon as possible.
Please make sure you read, understand and abide by the Academic Integrity Code for the Faculty and College of Arts and Sciences.
Students With Disabilities
If you have a disability for which you are or may be requesting an
accommodation, you are encouraged to contact both your instructor and
Disability Resources and Services, 216 William Pitt Union, (412)
648-7890/(412) 383-7355 (TTY), as early as possible in the term. DRS
will verify your disability and determine reasonable accomodations for
this course.
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