Discrete Structures - (Mathematics Code)

Discrete Structures - (Mathematics Code) Course Menu

This course is designed for students in math and computer science. Logic is emphasized in this course, and topics include: proof and theory including inductive and deductive proofs, propositional and predicate logic and calculus, set theory, algorithms including recursion, trees, relations and functions, counting and probability, and elements of the theory of directed and undirected graphs including Dijkstra's shortest path algorithm. Additionally, an introduction to complexity of algorithms and recurrence relations is included. Upon completion, students will be able to solve real world problems and use appropriate models for analysis.
Prerequisite: College Algebra or Precalculus with a grade of C or better.

Chapter 1

Logic

Lessons Homework HW Quiz
1.1   Non-Linear Inequalities 1.1 1.1
1.2   Truth Tables & Propositions 1.2 1.2
1.3   Logic Operators 1.3 1.3
1.4   Quantifiers - Part 1 1.4 1.4
1.5   Quantifiers - Part 2 1.5 1.5

Chapter 1 Test - (23 online, 11 essay questions)

 

Chapter 2

Formal Proofs

Lessons Homework HW Quiz
2.1   Truth Tables 2.1 2.1
2.2   Direct Proof 2.2 2.2
2.3   Proof by Contradiction 2.3 2.3
2.4   Proof by Contrapositive 2.4 2.4
2.5   If and only if Proof 2.5 2.5
2.6   Proof by Induction 2.6 2.6

Chapter 2 Test - (9 online, 8 essay questions)

 

Chapter 3

Sets and Relations

Lessons Homework HW Quiz
3.1   Introduction to Sets 3.1 3.1
3.2   Venn Diagrams 3.2 3.2
3.3   Relations 3.3 3.3
3.4   Equivalence Relations 3.4 3.4
3.5   Matrices of Relations 3.5 3.5
3.6   Functions 3.6 3.6
3.7   Sequences & Series 3.7 3.7

Chapter 3 Test - (28 online, 13 essay questions)

 

Chapter 4

Algorithms

Lessons Homework HW Quiz
4.1   Introduction to Algorithms 4.1 4.1
4.2   The Euclidean Algorithm 4.2 4.2
4.3   Recursive Algorithms 4.3 4.3
4.4   Complexity of Algorithms 4.4 4.4

Chapter 4 Test - (18 online, 6 essay questions)

 

Chapter 5

Graph Theory

Lessons Homework HW Quiz
5.1   Introduction to Graph Theory 5.1 5.1
5.2   Cycle and Paths 5.2 5.2
5.3   Hamiltonian Cycles 5.3 5.3
5.4   Matrices of Relations 5.4 5.4
5.5   Dijkstra's Algorithm 5.5 5.5
5.6   Isomorphic Graphs 5.6 5.6
5.7   Planar Graphs 5.7 5.7

Chapter 5 Test - (27 online, 9 essay questions)

 

Chapter 6

Trees

Lessons Homework HW Quiz
6.1   Introduction to Trees 6.1 6.1
6.2   Depth First Search Algorithm 6.2 6.2
6.3   Breath First Search Algorithm 6.3 6.3
6.4   Minimal Spanning Trees 6.4 6.4

Chapter 6 Test - (7 online, 6 essay questions)

 

Chapter 7

Recurrence Relations and Finite-State Machines

Lessons Homework HW Quiz
7.1   Introduction to Recurrence Relations 7.1 7.1
7.2   Solving Recurrence Relations 7.2 7.2
7.3   Introduction to Finite-State Machines 7.3 7.3

Chapter 7 Test - (8 online, 9 essay questions)

 

Chapter 8

Counting and Probability

Lessons Homework HW Quiz
8.1   Counting 8.1 8.1
8.2   Permutations and Combinations 8.2 8.2
8.3   Finite Basic Probabilities 8.3 8.3
8.4   Basic Probability Laws 8.4 8.4

Chapter 8 Test - (31 online, 0 essay questions)

 

Final for Discrete Structures - (44 online, 16 essay questions)

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