12/21/2024 5:49:48 PM	MATH 10 Course Outline as of Summer 2019	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  MATH 10	Title:  NATURE OF MATH
Full Title:  Nature of Mathematics
Last Reviewed:9/23/2024

Units		Course Hours per Week			Nbr of Weeks	Course Hours Total
Maximum	3.00	Lecture Scheduled	3.00		17.5 max.	Lecture Scheduled	52.50
Minimum	3.00	Lab Scheduled	0		6 min.	Lab Scheduled	0
		Contact DHR	0			Contact DHR	0
		Contact Total	3.00			Contact Total	52.50
		Non-contact DHR	0			Non-contact DHR Total	0

Total Out of Class Hours:  105.00

Total Student Learning Hours: 157.50

Title 5 Category:  AA Degree Applicable
Grading:  Grade or P/NP
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly: 

Catalog Description:

A survey course in mathematical concepts and mathematics in culture. Topics to include mathematical reasoning and four additional topics selected from number theory, probability, statistics, mathematical modeling, contemporary applications, geometry, and the history of mathematics. Recommended for liberal arts students.

Prerequisites/Corequisites:
Completion of MATH 161 or MATH 154 or MATH 156 or MATH 155 or AB705 placement into Math Tier 1 or higher

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

A survey course in mathematical concepts and mathematics in culture. Topics to include mathematical reasoning and four additional topics selected from number theory, probability, statistics, mathematical modeling, contemporary applications, geometry, and the history of mathematics. Recommended for liberal arts students.

(Grade or P/NP)
Prerequisites:Completion of MATH 161 or MATH 154 or MATH 156 or MATH 155 or AB705 placement into Math Tier 1 or higher
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:		Effective:	Fall 1981	Inactive:
Area:	B MC	Communication and Analytical Thinking Math Competency
CSU GE:	Transfer Area			Effective:	Inactive:
	B4	Math/Quantitative Reasoning		Fall 1981
IGETC:	Transfer Area			Effective:	Inactive:
	2A	Mathematical Concepts & Quantitative Reasoning		Fall 1981
CSU Transfer:	Transferable	Effective:	Fall 1981	Inactive:
UC Transfer:	Transferable	Effective:	Fall 1981	Inactive:
C-ID:

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:

1.  Apply the principles of inductive and deductive reasoning.

2.  Demonstrate proficiency in mathematical skills and conceptual understanding within four

     of the following topics:  number theory, probability, statistics, mathematical modeling,

    contemporary applications, geometry, and the history of mathematics.

3.  Apply mathematical concepts to a variety of real-world problems.

 

Objectives:

At the conclusion of this course, the student should be able to:

1. Define inductive reasoning, and apply to patterns and sequences.

2. Define deductive reasoning, and apply to logic and sets.

3. Demonstrate ability to perform four of the following objectives:

    A. Define various sets of numbers and use number systems of different bases.

    B. Apply counting techniques, permutations, combinations, and probability models.

    C. Define frequency distributions and measures of central tendency and dispersion, and create

         graphical displays of data.

    D. Apply mathematical models such as linear, quadratic, exponential, and logarithmic, to

         real-world problems.

    E. Understand topics within contemporary mathematics, such as voting and apportionment,

         financial mathematics, graph theory, linear programming, and applications of matrices.

    F. Define and apply concepts of areas, volumes, Euclidean and non-Euclidean geometry, and

         selected other topics in geometry.

    G. Describe the historical development of mathematics, the role of theorem and proof in

         mathematical thought, and significant mathematical results and mathematicians.

Topics and Scope

I. Mathematical Reasoning

    A. Inductive reasoning

         1. Patterns

         2. Sequences

    B. Deductive reasoning

         1. Logic

         2. Sets

 

Four additional topics chosen from II through VIII.

 

II. Number Theory

    A. Sets of numbers (e.g. prime, perfect, amicable, etc.)

    B. Numeration systems and number bases

    C. Additional topics may be chosen from identification numbers, encoding data,

         modular arithmetic, and cardinal numbers

III. Probability

    A. Counting techniques

    B. Rules of probability

    C. Conditional probability

    D. Probability models and simulations

IV. Statistics

    A. Frequency distributions

    B. Measures of central tendency and dispersion

    C. Graphical display of data

    D. Additional topics may be chosen from normal curve, estimation, and margin

          of error

V. Mathematical Modeling

    A. Linear, quadratic, exponential, and logarithmic models

    B. Regression models

VI. Contemporary Applications - Types of Applications to be Chosen by Instructor, but Could

    Include One or More of the Following:

    A. Linear programming

    B. Matrices

    C. Financial mathematics

    D. Voting and apportionment

    E. Graph theory

VII. Geometry

    A. Areas and volumes

    B. Euclidean geometry and deductive systems

    C. Non-Euclidean geometry

    D. Additional topics may be chosen from conic sections, trigonometry, fractal

         geometry, polyhedra, symmetry and tesselations

VIII. History and Culture of Mathematics

    A. Overview of the historical development of mathematics

    B. Role of theorem and proof in mathematical thought

    C. Significant mathematical results and mathematicians

Assignments:

1. Reading outside of class (approximately 20-50 pages per week)

2. Problem set assignments from required text(s) or supplementary materials chosen by the

    instructor (approximately 1-6 per week)

3. Quizzes (approximately 0-4 per week)

4. Exams (3-8)

5. Projects (for example computer explorations or modeling activities (0-10)

Methods of Evaluation/Basis of Grade.

Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.		Writing 0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.		Problem Solving 5 - 25%
Problem sets, projects
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.		Skill Demonstrations 0 - 0%
None
Exams: All forms of formal testing, other than skill performance exams.		Exams 75 - 95%
Exams and quizzes
Other: Includes any assessment tools that do not logically fit into the above categories.		Other Category 0 - 0%
None

Representative Textbooks and Materials:

Thinking Mathematically. 6th ed. Blitzer, Robert. Pearson. 2014 (classic)

Mathematics: A Practical Odyssey. 7th ed. Johnson, David and Mowry, Thomas. Cengage. 2012 (classic)

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