Chabot College
Course Outline for Mathematics 40
CONCEPTS OF MATHEMATICS
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Catalog Description:
MTH 40 - Concepts of Mathematics
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3.00 units
Investigation of the nature of mathematics as a human endeavor and an examination of important concepts
of mathematics.
Prerequisite: MTH 54 , MTH 54L , MTH 55 , MTH 55L or , MTH 55B (completed with a grade of "C" or
higher) or an appropriate skill level demonstrated through the Mathematics Assessment process.
Units
Contact Hours
Week
Term
3.00
Lecture
Laboratory
Clinical
Total
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3.00
3.00
0
0.00
3.00
3.00
0
0.00
3.00
Prerequisite Skills:
Before entry into this course, the student should be able to:
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solve exponential equations using logarithms;
find inverse functions and compose functions in the context of real data;
find linear system models for data and interpret solutions to these linear systems;
solve quadratic equations by factoring, completing the square, and quadratic formula;
sketch the graphs of functions and relations:
a. algebraic, including polynomial and rational
b. logarithmic
c. exponential
d. circles;
perform function composition;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational exponents;
sketch the graphs of functions and relations:
a. logarithmic
b. exponential
c. circles;
find and sketch inverse functions;
perform function composition;
solve exponential and logarithmic equations;
apply the concepts of logarithmic and exponential functions;
solve quadratic equations by factoring, completing the square, and quadratic formula;
sketch the graphs of functions and relations:
a. algebraic, including polynomial and rational
b. logarithmic
c. exponential
d. circles;
solve exponential and logarithmic equations;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational exponents;
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Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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Course Content:
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Geometry
A. Non Euclidean
B. Three dimensional Euclidean geometry (Platonic solids)
Modern Algebra
Number theory
Probability and Statistics
At least two of the following additional topics must be explored (no more than 40% of the course):
A. Real and complex numbers
B. Dynamical systems
C. Topology
D. Mathematical systems (groups, rings, and fields)
E. Boolean algebra
F. Applied mathematics (in biology, physics, business, or other)
G. Logic
Methods of Presentation
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apply principles from algebra and elementary number theory to current technology, such as those
used in encryption techniques;
identify the similarities and differences between Euclidean and non-Euclidean geometries;
explore and find certain relationships between geometry and topology;
build Platonic solids and describe their properties;
determine the cardinality of the set of Platonic solids;
apply problem-solving techniques learned in one area to another;
measure uncertainty using the principles of probability;
systematically count all possible outcomes using permutations and combinations;
identify misleading statistics.
Lecture/Discussion
Small and large group work
Student presentations
Audio-visual presentations
Resources available on CD’s or on the Internet
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
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Journal participation- In your journal, construct a Golden Rectangle (using the method we
went over in class and as directed in your book on pages 40, 241). Now make a separate
paper copy of a Golden Rectangle that is at least 6 inches on its shorter side. In that large
Golden Rectangle, find the largest square and move it (cut it off). Measure the dimensions
of the remaining rectangle. Record these numbers. In that same remaining rectangle, find
the larges square inside and cut that square off. Measure the dimensions of what is left (it
should be a rectangle and it should look familiar!) Record these numbers in your journal
and state what relationship they have, relevant to the Golden Rectangle.
Homework problems from the textbook- Suppose we start with one pair of baby rabbits,
and again they create a new pair every month, but this time let’s suppose that it takes two
months before a pair of bunnies is mature enough to reproduce. Make a table for the first
10 months, indicating how many pairs there would be at the end of each month. Do you
see a pattern? Describe a general formula for generating the sequence of rabbit-pair
counts.
2. Methods of Evaluating Student Progress
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Exams/Tests
Quizzes
Projects
Final Examination
Textbook (Typical):
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Burger, Edward B. and Michael Starbird (2005). The Heart of Mathematics Key Curriculum Press.
Special Student Materials
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Toolkit of manipulatives (included with texts such as The Heart of Mathematics)
Student journal