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Course Syllabus

MATH2305 - Discrete Mathematics

Catalog Description: A study of set theory, relations, functions, matrices, number systems, number theory, difference equations, graphs and trees, combinatorics, probability, and Boolean Algebra. Lecture Hrs = 3, Lab Hrs = 0

Semester Credit Hours: 3
Lecture Hours per Week:
Contact Hours per Semester: 48
State Approval Code: 2701015137

Course Subject/Catalog Number: MATH 2305
Course Title: Discrete Mathematics

Instructional Goals and Purposes:

Lee College’s instructional goals include (1) creating an academic atmosphere in which students may develop their intellects and skills and (2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.

General Course Objectives:

Successful completion of this course will promote the general student learning outcomes listed below. The student will be able

  1. To apply problem-solving skills through solving application problems.
  2. To demonstrate arithmetic and algebraic manipulation skills.
  3. To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.
  4. To construct appropriate mathematical models to solve applications.
  5. To interpret and apply mathematical concepts.
  6. To use multiple approaches – physical, symbolic, graphical and verbal – to solve application problems

Specific Course Objectives:

Upon successful completion of the course, the student will be able to

  1. Perform set operations and show the relationships between number systems.
  2. Evaluate, compose, compare, and contrast functions, relations, recursion and algorithms.
  3. Assess the validity of logical expressions.
  4. Apply the basic combinatorics formulas to counting problems.
  5. Compare and contrast algorithm complexity for common algorithms.
  6. Construct and explain some basic proofs.
  7. Perform proofs using induction.
  8. Apply the concept of graphs, trees, paths, and circuits to real world situations.
  9. Represent networks and relationships through the use of graphs and trees.
  10. Perform and evaluate search problems and sorting algorithms.
  11. Examine the mathematical contributions made by people from diverse cultures throughout history.
  12. Articulate a solution to mathematical problems.
  13. Apply appropriate technology to the solution of mathematical problems.

Course Content:

Students will be required to do the following:

  1. Set Theory
    1. Use listing notation, descriptive notation, and set builder notation to describe a set.
      1. Find the union, intersection, and the symmetric difference of two sets.
      2. Find the complement of a set.
      3. Find the Cartesian Product of two sets.
      4. State and apply DeMorgan’s laws.
  2. Logic and Proofs
    1. Calculate truth values of propositions.
    2. Determine if two propositions are logically equivalent.
    3. Differentiate between universal and existential quantifiers.
    4. Analyze an argument.
    5. Understand the different methods of proof; such as direct, proof by contrapositive, and proof by contradiction.
    6. Write a proof to a given statement.
  3. Language of Mathematics
    1. Determine if a relation is reflexive, antireflexive, symmetric, or transitive.
    2. Determine if a given relation defines an equivalence relation.
    3. Given a relation on a set S, describe the different equivalence classes.
    4. Determine if a function f is well-defined.
    5. Given an integer n, determine its congruence class mod p, where p is a positive integer.
    6. Draw a digraph for a given relation.
    7. Find a matrix for a given digraph.
  4. Algorithms
    1. Analyze algorithms.
    2. Prove a statement using mathematical induction.
    3. Analyze sequences using Big-Oh notation.
    4. Analyze recursive algorithms and relations.
    5. Use the Euclidean Algorithm to determine the greatest common divisor between two integers.
  5. Counting Methods
    1. Solve application problems concerning permutations and combinations.
    2. Solve basic probability problems.
    3. Use the Inclusion-Exclusion Principle for counting unions of more than two sets.
    4. Use the Binomial Theorem to evaluate an nth power of a binomial.
    5. Solve counting problems involving ordered partitions.
    6. Solve counting problems that require the Pigeon-Hole Principle.
    7. Solve applications involving conditional probability.
    8. Find probabilities involving independent events.
  6. Graph Theory
    1. Write the definition of and recognize a simple graph, Euler circuit, tree, spanning tree, leaves, and a rooted tree
    2. Write the definition of the degree of a vertex.
    3. Write a definition for a Hamilton path and a Hamilton circuit.
    4. Determine the length of the shortest path connecting a given pair of vertices.
    5. Describe an isomorphism between two given graphs.
    6. Analyze Euler Circuits.
    7. Describe an isomorphism between two given trees.
    8. Determine if a graph has a Hamilton path.
    9. Determine if a graph is a Hamilton circuit.

Methods of Instruction/Course Format/Delivery:

Faculty may choose from but are not limited to the following methods of instruction: lecture, discussion, Internet, video, television, demonstrations, field trips, collaboration, readings.

Assessment:

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities.   Faculty may choose from the following methods:  

  • Attendance
  • Book reviews
  • Class preparedness and participation
  • Collaborative learning projects
  • Compositions
  • Exams/tests/quizzes
  • Homework
  • Internet  
  • Journals
  • Library assignments
  • Readings
  • Research papers
  • Scientific observations
  • Student-teacher conferences
  • Written assignments

Course Grade:

Students' final grades are determined by:
100-90 A
89-80 B
79-70 C
69-60 D
59 or below F

Texts, Materials, and Supplies:

For current texts and materials, use the following link to access bookstore listings:   http://www.leecollegebooks.com

Other: