MATH 2000 - Discrete Mathematics

Academic Division:

Liberal Arts

Academic Discipline:

Mathematics

Assistant Dean: Steve Haynes PhD

3 Credit(s)
This course presents topics in sets, logic, proofs, functions/sequences/relations, algorithms, counting methods, recurrence relations, graph theory, and trees. Emphasis is placed on proper notation and terminology as well as problem solving and proofs. Prerequisite MATH 1110 (minimum grade of C- required) or COMPASS College Algebra score of 46 or higher or ACT math score of 26 or higher or ACCUPLACER College Level Math Score of 55 or higher. UG

3 Lecture Hour(s);

Required Prerequisite Course(s): Successful completion of MATH 1110 with a grade of C- or better or ACT Math score of 26 or higher or ACCUPLACER Next Generation Algebra 263 or above

College Wide Outcomes

College-Wide Learning Outcomes	Assessments - - How it is met & When it is met
Communication – Written
Communication – Speech
Intercultural Knowledge and Competence
Critical Thinking
Information Literacy
Quantitative Literacy	Cumulative Review Problem Sets: Weeks 3,7,11 Quantitative Literacy VALUE Rubric Tests: Weeks 4,8,12; Final Exam: Week 16

Student Learning Outcomes for Course

Outcomes	Assessments – How it is met & When it is met
1. Find sets/subsets based upon given criteria	HW:Wk#1 Test:Wk#4 F.Ex.:Wk#16
2. Perform unary and binary set operations both symbolically and visually	HW:Wk#1 Test:Wk#4 F.Ex.:Wk#16
3. Use quantifiers when describing set relationships	HW:Wk#2 Test:Wk#4 F.Ex.:Wk#16
4. Analyze simple or compound propositions by using truth tables and/or Venn diagrams	HW:Wk#1 Test:Wk#4 F.Ex.:Wk#16
5. Analyze arguments using rules of inference.	HW:Wk#2 Test:Wk#4 F.Ex.:Wk#16
6. Describe and use methods of proof including direct proofs, indirect proofs, resolution proofs, and mathematical induction	HW:Wk#3,4 Test:Wk#4 F.Ex.:Wk#16
7. Provide examples of and/or identify functions that are injections, surjections, bijections, and composite functions	HW:Wk#1 Test:Wk#8 F.Ex.:Wk#16
8. Find terms of a sequence, both specific terms and the general term	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
9. Define sequences and answer questions about them	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
10. Define strings and answer questions about them	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
11. Compute the resulting string from string operations	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
12. Prove or disprove discrete mathematical assertions	HW throughout the course
13. Verify characteristics of relations	HW:Wk#5 Test:Wk#8 F.Ex.:Wk#16
14. Use digraphs to describe relations	HW:Wk#6 Test:Wk#8 F.Ex.:Wk#16
15. Use matrices to describe relations	HW:Wk#6 Test:Wk#8 F.Ex.:Wk#16
16. Define and analyze algorithms, including recursive algorithms	HW:Wk#6,7 Test:Wk#8 F.Ex.:Wk#16
17. Use counting techniques including permutations and combinations to compute the number of ways an event can occur	HW:Wk#8,9 Test:Wk#12 F.Ex.:Wk#16
18. Calculate discrete probabilities	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
19. Compute binomial coefficients, with and without using Pascal’s triangle	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
20. Prove combinatorial identities	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
21. Solve problems by using the Pigeonhole Principle	HW:Wk#10 Test:Wk#12 F.Ex.:Wk#16
22. Use recurrence relations to analyze the times algorithms require	HW:Wk#11 Test:Wk#12 F.Ex.:Wk#16
23. Define both directed and undirected graphs in terms of vertices and edges and visually represent these graphs	HW:Wk#12 F.Ex.:Wk#16
24. Identify paths and cycles in a graph or sub-graph	HW:Wk#12 F.Ex.:Wk#16
25. Recognize graphs with/without Euler cycles and Hamiltonian cycles	HW:Wk#13 F.Ex.:Wk#16
26. Define and recognize trees	HW:Wk#13 F.Ex.:Wk#16
27. Show the relationship of a tree to Huffman codes	HW:Wk#13 F.Ex.:Wk#16
28. Characterize trees using proper terminology	HW:Wk#13 F.Ex.:Wk#16
29. Find spanning trees and minimal spanning trees	HW:Wk#14 F.Ex.:Wk#16
30. Analyze combinatorial circuits	HW:Wk#14 F.Ex.:Wk#16
31. Represent circuits using Boolean Algebra expressions	HW:Wk#15 F.Ex.:Wk#16
32. Use Boolean Algebra to synthesize circuits	HW:Wk#15 F.Ex.:Wk#16

Standard Grading Scale
93-100 A

90 - 92 A-

87- 89 B+

83 - 86 B

80 -82 B-

77- 79 C+

73 - 76 C

70 -72 C-

67- 69 D+

63 - 66 D

60 -62 D-

00- 59 F

Statement on Diversity
North Central State College believes that every student is a valued and equal member of the community.* Every student brings different experiences to the College, and all are important in enriching academic life and developing greater understanding and appreciation of one another. Therefore, NC State College creates an inclusive culture in which students feel comfortable sharing their experiences. Discrimination and prejudice have no place on the campus, and the College takes any complaint in this regard seriously. Students encountering aspects of the instruction that result in barriers to their sense of being included and respected should contact the instructor, assistant dean, or dean without fear of reprisal.

*Inclusive of race, color, religion, gender, gender identity or expression, national origin (ancestry), military status (past, present or future), disability, age (40 years or older), status as a parent during pregnancy and immediately after the birth of a child, status as a parent of a young child, status as a foster parent, genetic information, or sexual orientation,

Standard NCSC Course Policies
Important information regarding College Procedures and Policies can be found on the syllabus supplement located at this link