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MAT 253 Discrete Mathematics

This course covers discrete models, sets, functions, logic, mathematical induction, algorithms, relations, graphs, and trees.

Credits

3

Prerequisite

Prerequisite: MAT 183 or MAT 193 or MAT 281

See Course Syllabus

Course Number and Title:

MAT 253 Discrete Mathematics

Campus Location

  • Dover
  • Georgetown
  • Stanton
  • Wilmington

Prerequisites

Prerequisite: MAT 183 or MAT 193 or MAT 281

Course Credits and Hours

3 credit(s)

3 lecture hours/week

0 lab hours/week

Course Description

This course covers discrete models, sets, functions, logic, mathematical induction, algorithms, relations, graphs, and trees.

Additional Materials

Scientific Calculator or Graphing Calculator: TI 83 or TI 84

Required Text(s)

Obtain current textbook information by viewing the campus bookstore - https://www.dtcc.edu/bookstores online or visit a campus bookstore. Check your course schedule for the course number and section.

Core Course Performance Objectives (CCPOs)

  1. Apply set theory in mathematical reasoning. (CCC 2, 6)
  2. Apply logic to determine equivalent statements and the validity of arguments. (CCC 2, 6)
  3. Apply patterns and induction to generalize mathematical concepts. (CCC 2, 6)
  4. Explain the nature of axiomatic systems and apply basic operations in modular systems. (CCC 1, 2, 6)
  5. Apply fundamental concepts in graph theory. (CCC 2, 6)

See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.

Measurable Performance Objectives (MPOs)

Upon completion of this course, the student will:

  1. Apply set theory in mathematical reasoning.
    1. Write a set using set-builder notation.
    2. Identify a subset and a proper subset of a given set.
    3. Given a universal set, find the complement of a subset.
    4. Find the intersection and union of two or more sets.
    5. Use Venn diagrams to show relationships between sets.
    6. Determine the Cartesian product of two sets.
    7. Sort and analyze data using Venn diagrams.
  2. Apply logic to determine equivalent statements and the validity of arguments.
    1. Translate English statements to symbolic logic notation and vice-versa.
    2. Construct truth tables for logic statements.
    3. Determine whether two statements are logically equivalent or contradictory.
    4. Write the contrapositive, inverse, and converse of a given conditional statement.
    5. Determine whether the form of an argument is valid.
    6. Write the symbolic statement for a given network and construct a switching network for a given symbolic statement.
  3. Apply patterns and induction to generalize mathematical concepts.
    1. Generate the terms of a sequence or series from a given formula.
    2. Determine explicit formulas for a given sequence.
    3. Determine recursive formulas for arithmetic and geometric sequences.
    4. Identify the nth term of an arithmetic sequence.
    5. Find the sum of finite series.
    6. Solve application problems using series and sequences.
    7. Use mathematical induction to prove statements about integers.
  4. Explain the nature of axiomatic systems and apply basic operations in modular systems.
    1. Perform modular arithmetic.
    2. Identify the parts of an axiomatic system.
    3. Convert a numeral to and from base 10.
    4. Convert a numeral between binary, hexadecimal, and octal bases.
    5. Perform addition, subtraction, and multiplication in non-decimal bases.
  5. Apply fundamental concepts in graph theory.
    1. Identify components of a graph.
    2. Represent real-world situations with graphs.
    3. Determine whether graphs have Euler or Hamiltonian circuits.
    4. Determine whether walks are also trails, paths, or simple circuits.
    5. Determine the chromatic number of a graph.

Evaluation Criteria/Policies

The grade will be determined using the Delaware Tech grading system:

90-100 = A
80-89 = B
70-79 = C
0-69 = F
Students should refer to the Catalog/Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.

Final Course Grade

Calculated using the following weighted average

Evaluation Measure

Percentage of final grade

5 Tests (summative) (equally weighted)

70%

Project (summative)

10%

Homework (formative)

10%

Formative (quizzes, activities)

10%

TOTAL

100%

Core Curriculum Competencies (CCCs are the competencies every graduate will develop)

  1. Apply clear and effective communication skills.
  2. Use critical thinking to solve problems.
  3. Collaborate to achieve a common goal.
  4. Demonstrate professional and ethical conduct.
  5. Use information literacy for effective vocational and/or academic research.
  6. Apply quantitative reasoning and/or scientific inquiry to solve practical problems.

Students in Need of Accommodations Due to a Disability

We value all individuals and provide an inclusive environment that fosters equity and student success. The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. The College's policy on accommodations for persons with disabilities can be found in the College's Guide to Requesting Academic Accommodations and/or Auxiliary Aids Students may also access the Guide and contact information for Disabilities Support Counselors through the Student Resources web page under Disabilities Support Services, or visit the campus Advising Center.

Minimum Technology Requirements

Minimum technology requirements for all distance education type courses.

Academic Integrity

https://dtcc.smartcatalogiq.com/Current/Catalog/Academics/Academic-Integrity

Attendance

https://dtcc.smartcatalogiq.com/Current/Catalog/Search?q=attendance

Cell phone/Electronic Device

https://dtcc.smartcatalogiq.com/Current/Catalog/Student-Policy/Cell-Phone-and-Electronic-Device-Policy

Tuition Adjustment Policy

https://dtcc.smartcatalogiq.com/Current/Catalog/Financial/Tuition-Fee-Adjustment-Policy-Course-or-Semester-Withdrawal