COMMON COURSE OUTLINE:
1. Math 1111
2. Contemporary Concepts in Mathematics
3. 3
credits
4. 3 hours per week
5. Prerequisites:
1. Appropriate ASAP score or C or higher in Math
0098
2. Reading ASAP score of at
least 27
3. Writing ASAP score of at
least 22
MNTC: Goal 2: Critical Thinking (CT), Goal 4: Mathematics/Logical
Reasoning (MA)
A Liberal
Arts course for the student who wishes to acquire a broad background in
mathematics without taking the usual sequences of specialized courses. These topics will be
covered: Geometry, Logic, Finance
Mathematics, Probability, Statistics, and Problem Solving. Other topics will be selected from the
following list and may vary, depending on the instructor and/or the text: Numeration Systems, Trigonometry, Voting
Methods, Apportionment, Graph Theory, Sets, Discrete Mathematics, Number
Theory, and Game Theory. Grading is A-F.
C. RECOMMENDED ENTRY SKILLS/KNOWLEDGE:
1. Solve linear equations
2. Add, subtract, and multiply
polynomials
3. Apply the laws of exponents
4. Operations with rational
expressions
5. Convert between standard and
scientific notation
6. Apply the Pythagorean
Theorem
D. MAJOR CONTENT AREAS (to be covered by all
instructors, regardless of textbook):
1. Geometry
2. Logic
3. Finance Mathematics
4. Probability
5. Statistics
6. Problem
Solving
E.
OTHER CONTENT AREAS (instructor’s
choice) TO BE SELECTED FROM:
1. Numeration systems
2. Trigonometry
3. Voting Methods
4. Apportionment
5. Graph Theory
6. Sets
7. Discrete
Mathematics
8. Number
Theory
9. Game Theory
F.
LEARNING OUTCOMES: MNTC
a. illustrate historical and
contemporary applications of mathematical/logical systems
b. clearly express
mathematical/logical ideas in writing
c. explain what constitutes a
valid mathematical/logical argument (proof)
d. apply higher-order
problem-solving and/or modeling strategies
a. gather factual information and
apply it to a given problem in a manner that is relevant, clear, comprehensive,
and conscious of possible bias in the information selected.
b. imagine and seek out
a variety of possible goals, assumptions, interpretations, or perspectives,
which can give alternative meanings or solutions to given situations or
problems.
c. analyze the logical
connections among the facts, goals, and implicit assumptions relevant to a
problem or claim; generate and evaluate implications that follow from them.
d. recognize and
articulate the value assumptions which underlie and affect decisions,
interpretations, analyses, and evaluations made by ourselves and others.
3. Major Content Area Outcomes.
Students will be able to
a. understand the difference between Euclidean
and non-Euclidean geometries and apply the principles of both.
b. understand the difference between inductive
and deductive reasoning and apply both to problem solving.
c. understand and apply the principles of
symbolic logic.
i. recognize a statement in logic.
ii. negate a statement in logic.
iii. find the inverse, the converse, and the
contrapositive of a given statement.
iv. apply DeMorgan’s
laws.
v. translate English statements to symbolic
form.
vi. understand and apply the basic
syllogistic forms to determine whether an argument is valid.
vii. make truth tables to determine if two
statements are logically equivalent.
viii. make truth tables to determine if an
argument is valid.
d. apply the formulas of finance to real world
problems.
i. apply the simple interest formulas.
ii. apply the compound
interest formula.
iii. apply the formula for ordinary annuities.
iv. apply the formula for loans.
v. solve any of the finance formulas for any of
the variables.
vi. understand the
difference between nominal and effective rates.
e. calculate probabilities and analyze games of
chance.
i. apply all of the four counting methods
(listing, multiplication rule, combinations, and permutations) to
determine possible outcomes.
ii.
understand the difference between probability
and odds.
iii.
calculate probability and odds.
iv.
calculate probabilities of compound events.
v. calculate conditional probabilities.
vi.
understand the definition of a fair
game.
vii.
calculate expected value.
f. interpret data and its presentation.
i. interpret data that is presented in any of
the types of graphs, charts, or frequency distributions.
ii.
calculate measures of central tendency (mean,
median, mode).
iii.
calculate measures of dispersion (range and
standard deviation).
iv.
understand and solve problems involving the
normal distribution.
v. understand the application of inferential
statistics in society.
vi.
calculate margin of error, confidence
intervals, and confidence levels.
g. apply
common strategies for problem solving.
4.
Other Content Areas – (these will
vary depending on the topics selected.)
a. apply the basic
principles of trigonometry to real world problems.
b. use set theory notation and apply the
operations of sets and Venn diagrams.
c. use
some of the voting methods such as majority rule, the plurality method, binary voting,
Condorcet winner, and the Forda method.
d. apply
the basic principles of graph theory.
e. apply
and analyze game strategies.
f. illustrate historical and contemporary
applications of numeration systems.
G. METHODS FOR EVALUATION OF STUDENT LEARNING:
1. Tests and/or
2. Quizzes and/or
3. Homework and/or
4. Cooperative group work
and/or
5. Writing assignments and/or
6. Portfolios
H. SPECIAL INFORMATION (fees, directives on
hazardous materials, etc.):
A scientific calculator is
required.