Course Number and Title: MAT 253 Discrete Mathematics
This course covers discrete models, sets, functions, logic, mathematical induction, algorithms, relations, graphs, and trees.
TI-84 Graphing Calculator
- Apply set theory in mathematical reasoning. (CCC 2, 6)
- Apply logic to determine equivalent statements and the validity of arguments. (CCC 2, 6)
- Compute probabilities, combinations, and permutations. (CCC 2, 6)
- Apply patterns and induction to generalize mathematical concepts. (CCC 2, 6)
- Explain the nature of axiomatic systems and apply basic operations in modular systems. (CCC 1, 2, 6)
- 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.
Upon completion of this course, the student will:
- Apply set theory in mathematical reasoning.
- Write a set using set-builder notation.
- Identify a subset and a proper subset of a given set.
- Given a universal set, find the complement of a subset.
- Find the intersection and union of two or more sets.
- Use Venn diagrams to show relationships between sets.
- Determine the Cartesian product of two sets.
- Sort and analyze data using Venn diagrams.
- Apply logic to determine equivalent statements and the validity of arguments.
- Translate English statements to symbolic logic notation and vice-versa.
- Construct truth tables for logic statements.
- Determine whether two statements are logically equivalent or contradictory.
- Write the contrapositive, inverse, and converse of a given conditional statement.
- Determine whether the form of an argument is valid.
- Write the symbolic statement for a given network and construct a switching network for a given symbolic statement.
- Compute probabilities, combinations, and permutations.
- Calculate the probability of an event.
- Use the fundamental counting principle to calculate the probability of two or more events.
- Construct a tree diagram for a given experiment and use it to calculate probabilities.
- Calculate probabilities using the addition and multiplication rules.
- Determine the number of permutations and combinations for various scenarios.
- Solve related problems involving permutations and combination.
- Determine coefficients using the binomial theorem.
- Apply patterns and induction to generalize mathematical concepts.
- Generate the terms of a sequence or series from a given formula.
- Determine explicit formulas for a given sequence.
- Determine recursive formulas for arithmetic and geometric sequences.
- Identify the nth term of an arithmetic sequence.
- Find the sum of finite series.
- Solve application problems using series and sequences.
- Use mathematical induction to prove statements about integers.
- Explain the nature of axiomatic systems and apply basic operations in modular systems.
- Perform modular arithmetic.
- Identify the parts of an axiomatic system.
- Convert a numeral to and from base 10.
- Convert a numeral between binary, hexadecimal, and octal bases.
- Perform addition, subtraction, and multiplication in non-decimal bases.
- Apply fundamental concepts in graph theory.
- Identify components of a graph.
- Represent real-world situations with graphs.
- Determine whether graphs have Euler or Hamiltonian circuits.
- Determine whether walks are also trails, paths, or simple circuits.
- Determine the chromatic number of a graph.
Students must demonstrate proficiency on all CCPOs at a minimal 75 percent level to successfully complete the course. The grade will be determined using the Delaware Tech grading system:
Students should refer to the 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.
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
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. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.