Santa Monica College
Mathematics Department Addendum
Math 10/CS 10 – Discrete Structures
Prerequisite Comparison Sheet – exit skills of Math 8 and entry skills for Math 10
Exit Skills for Math 8
Upon successful completion of Math 10, the student will be able to:
A.
Differentiate and integrate exponential, logarithmic, hyperbolic functions..
B.
Use various techniques of integrations and applications
C.
Analyze infinite series (congruence and divergence).
D.
Use Power and Taylor series to express an infinite series
E.
F.
Recognize indeterminant forms and improper integral (using polar coordinates or
parametric equations).
Use analytical geometry (rotation of axes) to differentiate and integrate
G.
Evaluate limits using L'Hopital's Rule.
H.
Find center of mass (centroid) and surface area.
:
Entry Skills for Math 10
Prior to enrolling in Math 10 students should be able to
1.
Differentiate and integrate exponential, logarithmic, hyperbolic functions. M8 (1)
.2.
Use various techniques of integrations and applications. M8 (2)
3.
Analyze infinite series (congruence and divergence). M8 (3)
4.
Use Power and Taylor series to express an infinite series. M8 (4)
5.
Recognize indeterminate forms and improper integral (using polar coordinates or
parametric equations). M8 (5)
6.
Use analytical geometry (rotation of axes) to differentiate and integrate. M8 (6)
7.
Know the binomial theorem. M2 (2)
Santa Monica College
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Santa Monica College
Student Learning Outcomes
Date: Fall 2009
Course Name and Number:
Math 10/CS 10 Discrete Structures
Student Learning Outcome(s):
 Individual faculty members will develop and reports on assessments for SLOs.
1.
Given a theoretical or applied problem, students will be able to represent the problem and
solve it using techniques such as combinatorics, graph theory, function theory and logic.
2.
Given a mathematical statement, students will be able to construct and communicate a valid
argument using standard proof techniques.
Demonstrate how this course supports/maps to at least one program and one institutional
learning outcome. Please include all that apply:
1.
Program Outcome(s):
“The student will demonstrate an appreciation and understanding of mathematics in order to
develop creative and logical solutions to various abstract and practical problems.”
As a result of learning about more advanced mathematical concepts, students will analyze
and solve abstract and practical problems.
2.
Institutional Outcome(s):
As a result of studying instructor feedback given during lecture, or written on homework and
exams, students will evaluate information critically and present solutions in a clear and
logical manner.
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Textbook: Roman, Steven, An Introduction to Discrete Mathematics, Harcourt, Brace, Jovanovich, Inc.,1989
A Sample Schedule for Math 10
This schedule assumes a standard meeting schedule of 1 hr 20 min with 2 class meetings per week.
Session
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Text Section/Activity
1.1 The Language of Sets
1.2 One-to-One Correspondences
1.3 Countable and Uncountable Sets
1.4 Functions
1.6 Proof by Contradiction
2.1 Statements, Connectives, and Symbolic Language
2.2 Truth Tables, Tautologies, and Contradictions
2.3 Logical Equivalence
2.4 Valid Arguments
2.5 Boolean Functions and Disjunctive Normal Form
2.6 Logic Circuits
2.7 Karnaugh Maps
3.1 Relations
3.2 Properties of Relations
Exam 1
3.3 Equivalence Relations
3.4 Partially Ordered Sets
3.5 More on Partially Ordered Sets: Maximal and Minimal Elements and
Topological Sorting
3.6 Order Isomorphisms (optional)
4.1 Introduction to Combinatorics
4.2 The Multiplication Rule
4.3 The Pigeonhole Principle
4.4 Permutations
4.5 More on Permutations
4.6 Combinations
4.7 Properties of the Binomial Coefficients
4.8 The Multinomial Coefficient
4.9 An Introduction to Recurrence Relations
4.10 Second Order Linear Nonhomogeneous Relations with Constant
Coefficients
4.11 Second Order Linear Nonhomogeneous Recurrence Relations
with Constant Coefficients (optional)
4.12 Generating Functions and Recurrence Relations (optional)
5.1 Permutations with Repetition
Exam 2
5.2 Combinations with Repetition
5.3 Linear Equations with Unit Coefficients
5.4 Distributing Balls into Boxes
5.5, 5.6 The Principle of Inclusion-Exclusion
5.7 The Principle of Inclusion-Exclusion
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Session
25
26
27
28
29
Text Section/Activity
5.8 An Introduction to Probability
6.1 Introduction to Graphs
6.2 Paths and Connectedness
6.3 Eulerian and Hamiltonian Graphs
6.5 Trees: The Depth First Search
6.7 Undirected Networks: The Minimal Spanning Tree Problem
6.9 Directed Networks: The Shortest Path Problem
Alternate Sample Schedule
Session
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Text Section/Activity
Text Section/Topic
1.1 Set Theory: Definitions, Notation, Examples
1.2, 1.4 Functions and One-to-One Correspondences
1.3 Countable Sets
1.3 Countable and Uncountable Sets
1.5, 1.6 Proofs by Induction and Contradiction
2.1, 2.2 Symbolic Logic, Truth Tables, Tautologies, Contradictions
2.3, 2.4 Logical Equivalence, Valid Arguments
2.5, 2.6, 2.7 Boolean Functions, Logic Circuits, Karnaugh Maps
3.1, 3.2 Relations on Sets: Definitions, Graphs, Properties
Exam 1
3.3 Equivalence Relations
3.4, 3.5 Partially Ordered Sets
3.x More with Equivalence Classes: Modular Arithmetic
4.2, 4.3 Multiplication Rule, Pigeonhole Principle
4.4, 4.5 Permutations
4.6 Combinations
4.7, 4.8 Binomial and Multinomial Coefficients
4.9, 4.10 Recurrence Relations
Exam 2
5.1, 5.2 Permutations and Combinations with Repetition
5.3 Linear Equations with Unit Coefficients
5.4, 5.5 Distributions, Principle of Inclusion-Exclusion (2 sets)
5.6, 5.7 Principle of Inclusion-Exclusion (more than 2 sets)
6.1, 6.2 Introduction to Graph Theory
6.2, 6.3 Connectedness, Eulerian Graphs
Exam 3
6.5, 6.7 Trees
6.6 Applications of Trees: Binary Search Trees, Huffman Codes
Review