Time: TH 11:00am-12:15pm 205 LAWRN
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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.
2 years of high school algebra.
Kenneth Rosen. Discrete Mathematics and Its Applications, 7th Edition , McGraw Hill Publishing Co., 2012.
|January 7||Administrivia, Propositional logic.||Section 1.1.||.|
|January 9||Propositional logic.||Sections 1.1-3.||Homework assigment 1|
|January 14||Predicate logic.||Sections 1.4.||.|
|January 16||Predicate logic.||Sections 1.4-5.||Homework assigment 2||January 21||Predicate logic. Formal and informal proofs||Sections 1.5-6.||.||January 23||Informal proofs||Sections 1.5-7.||Homework assigment 3||January 28||Sets and set operations||Sections 2.1-2.||.||January 30||Sets and set operations (cont.), Functions||Sections 2.1-3.||Homework assigment 4||February 4||Functions II.||Sections 2.1-3.||.||February 6||Sequences and summations||Sections 2.4.||Homework assigment 5||February 11||Countable and uncountable sets. Matrices.||Sections 2.5-6.||.||February 13||Matrices. Integers and division||Sections 2.6., 4.3.||Homework assigment 6||February 18||Integers and divisions. Congruency. CS applications.||Sections 4.3., 4.5.||.||February 20||Integers: Applications, base conversions. Mathematical induction.||Section 4.2., 4.5.||Homework assigment 7|
|February 25||Mathematical induction and recursion.||Chapter 5||.|
|February 27||Counting: basic counting rules.||Sections 6.1-2.||Homework assigment 8|
|March 4||Counting: permutations, combinations.||Chapter 6||.|
|March 6||Midterm exam||Chapters 1,2,4,5 and 6.1.||.|
|March 18||Midterm exam solutions||Chapters 1,2,4,5 and 6.1.||.|
|March 20||Counting: advanced counting methods. Probability||Sections 6.3-5; Chpater 7||Homework assigment 9|
|March 25||Probabilities.||Chapter 7||.|
|March 27||Probabilities: Bayes theorem, Bernoulli trial, Random variables, Expected value.||Chapter 7||Homework assigment 10|
Probabilities: expected value
|April 3||Relations II.||Chapter 9.1-3.||Homework assigment 11|
|April 8||Relations III||Chapters 9.1-3.||.|
|April 10||Relations IV. Graphs||Chapter 9.1-6.||Homework assigment 12|
|April 15||Graphs: graph types, graph properties||Chapter 10.||.|
|April 17||Graphs: Connectivity, Trees||Chapter 10.||.|
|April 26||Final exam||.|
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.
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