Course: Discrete Mathematics

Text: Discrete Mathematics Through Applications

Cost: $40.00

Prerequisite: Algebra II and teacher recommendation

Curricular goals interwoven throughout the mathematics program are that students will:

learn to communicate mathematically (QCC)

learn to use mathematics in their daily lives (QCC)

become proficient with appropriate computational tools and techniques (QCC)

learn to reason mathematically (QCC)

become mathematical problem solvers (QCC)

These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

Chapter 1: Election Theory (pp. 1-44)

· Determine election results using various procedures (QCC)(MADM_A2002-2)

· Identify paradoxes (QCC)(MADM_A2002-3)

· Use weighted voting, power indexes, and Arrow’s fairness criteria (QCC)(MADM_A2002-4)

· Interpret Arrow’s Impossibility Theorem (QCC)(MADM_A2002-5)

Chapter 2: Fair Division (pp. 45-102)

· Apply fair-division algorithms (QCC)(MADM_A2002-1)

· Identify methods of apportionment and apportionment paradoxes (QCC)(MADM_B2002-7)

Chapter 4: Graphs and Their Applications (pp. 151-212)

· Examine the structure of a graph (QCC)(MADM_B2002-6)

· Construct different representations of graphs (QCC)(MADM_B2002-7)

· Apply shortest path algorithms (QCC)(MADM_B2002-8)

· Analyze networks using graphs as models (QCC)(MADM_B2002-9)

· Solve problems involving the notions of connectedness, completeness, bipartiteness, planarity, and graph coloring (QCC)(MADM_B2002-10)

· Identify properties of graphs having circuits and/or paths (QCC)(MADM_B2002-11)

Chapter 5: More Graphs, Subgraphs and Trees (pp. 213-274)

· Apply definitions of a tree (QCC)(MADM_B2002-12)

· Find minimal spanning tree for a given graphs (QCC)(MADM_B2002-13)

· Solve problems involving the notions of connectedness, completeness, bipartitenes, planarity, and graph coloring (QCC)(MADM_B2002-10)

Chapter 3: Matrix Operations and Applications (pp. 103-150)

Ÿ Solve population growth and control problems using the Leslie model (QCC)(MADM_D2002-31)

Chapter 7: Matrices Revisited (pp. 345-406)

· Use powers of adjacency matrices to study connectivity properties of graphs and digraphs (QCC)(MADM_D2002-29)

· Solve probability problems using tree analysis by applying Markov’s algorithm (QCC)(MADM_D2002-30)

· Use the Leontif Input-Output model of an economy (QCC)(MADM_D2002-32)

Chapter 8: Recursion (pp. 407-471)

Ÿ Iterate first-order recurrence relations (QCC)(MADM_C2002-21)

Ÿ Develop the closed form of a first-order linear recurrence relation (QCC)(MADM_C2002-22)

Ÿ Apply process of iteration in different situations (QCC)(MADM_C2002-23)

Ÿ Analyze searching and sorting algorithms (QCC)(MADM_C2002-24)

Supplements to Book:

Sets

Ÿ Describe sets using appropriate notation and terminology (QCC)(MADM_E2002-33)

Ÿ Identify simple relations between sets (QCC)(MADM_E2002-34)

Ÿ Perform operations on sets (QCC)(MADM_E2002-35)

Ÿ Illustrate, and apply commutative laws, associative laws, distributive laws, and DeMorgan’s law (QCC)(MADM_E2002-36)

Ÿ Construct simple proofs using Venn Diagrams (QCC)(MADM_E2002-37)

Ÿ Determine power sets and Cartesian products of sets (QCC)(MADM_E2002-38)

Ÿ Determine sets are closed with respect to a given operation (QCC)(MADM_E2002-39)

Ÿ Investigate a variety of operations on various sets (QCC)(MADM_E2002-40)

Ÿ Identify group properties for given sets and operations (QCC)(MADM_E2002-41)

The Real Number System

Ÿ Examine the real number system (QCC)(MADM_F2002-42)

Ÿ Construct simple proofs about even and odd numbers (QCC)(MADM_F2002-43)

Ÿ Write an integer given in base 10 as a numeral in any base with emphasis on base 2 (QCC)(MADM_F2002-44)