Maui Community College
Course Outline
1. Alpha and Number MATH 100
Course Title Survey of Mathematics
Credits 3
Date of Outline October 2004
Course Description Acquaints the non-specialist with examples of mathematical reasoning. Explores selected topics such as numeration systems, consumer math, linear and exponential growth, inductive patterns, mathematical art, probability, statistics, set theory and logic.
2.
Contact Hours/Type 3 hours lecture per week
4. Prerequisites MATH 23 or 25 with at least a C or placement at MATH 100, and ENG 100 with at least a C (or concurrent), or consent.
Corequisites None
Recommended
Preparation
At least 11th grade reading skills.
Approved by _____________________________________ Date________________

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5. General Course Objectives
Maui Community College Standards:
Outcome 2.1
- Apply numeric, graphic, and symbolic skills and other forms of quantitative reasoning accurately and appropriately.
Outcome 2.2
- Demonstrate mastery of mathematical concepts, skills, and applications, using technology when appropriate.
Outcome 2.3
- Communicate clearly and concisely the methods and results of quantitative problem solving.
Outcome 2.4
- Formulate and test hypotheses using numerical experimentation.
Outcome 2.5
- Define quantitative issues and problems, gather relevant information, analyze that information, and present results.
Outcome 5.6 – Apply problem-solving techniques and skills, including the rules of logic and logical sequence.
Outcome 5.8 – Communicate clearly and concisely the methods and results of logical reasoning.
U H Manoa Symbolic Reasoning Hallmarks:
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Expose students to the beauty, power, clarity and precision of formal systems
Help students understand the concept of proof as a chain of inferences
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Teach students how to apply formal rules or algorithms
Require students to use appropriate symbolic techniques in the context of problem solving, and in the presentation and critical evaluation of evidence
Not focus solely on computational skills
Build a bridge from theory to practice and show students how to traverse this bridge
6.
Specific Course Objectives, Competencies, and Student Learning Outcomes
(This is a survey course. These specific course objectives, competencies and student learning outcomes are reflective of the spirit of this course and may be modified to meet the interests of a class with approval of the Math faculty)
For assessment purposes, these are linked to #7. Recommended Course Content.
On successful completion of this course, students will be able to a. understand the concept of percent and use in real-life situations b.
compute percent change and use to determine such things as percent
markup and down payment c. interpret circle graphs, bar graphs, and line graphs d.
differentiate between simple interest, compound interest and annuity
formulas and apply to real life experience

e. compute a discounted note f. create an amortization table g. compute values in a fixed installment loan h. compute APR for a fixed installment loan i.
calculate values used for investment or purchase using tables, formulas
and critical thinking skills j. use critical thinking skills for making decisions k. apply reasoning and problem-solving skills l. use inductive and deductive reasoning in problem-solving m. recognize and use mathematical patterns to solve problems n. hypothesize a conjecture based on number patterns o. use estimation to determine a range of reasonable solutions to
problems p. learn and apply the guidelines for problem solving (understand the
problem, devise a plan to solve the problem, carry out the plan, and
check the results)
q. gather, analyze, and make inferences (predictions) from numerical
information obtained in an experiment
r. recognize and understand the meanings of various statistical terms
s. recognize the misuses of statistics
t. create and interpret frequency distributions
u. create and interpret different types of statistical graphs (circle graphs,
histograms, frequency polygons)
v. compute and interpret the different measures of central tendency
(mean, median, mode, midrange) and determine which measure is
appropriate in a given circumstance.
w. compute and interpret the different measures of dispersion (range
and standard deviation)
x. create, interpret and solve normal distribution problems
y. recognize and understand the meanings of terms used in probability
z. differentiate between empirical and theoretical probability
aa. use expected value formula to develop an appreciation for
"expectation"
bb. create sample spaces
cc. use sample spaces to calculate probabilities
dd. calculate conditional probabilities
ee. generate arithmetic expressions needed to solve specific counting or
probability problems using permutations and combinations (factorials) ff.
recognize and understand the meanings of terms used in sets and logic gg.
use Venn Diagrams to determine equality of sets hh.
use Venn Diagrams to solve practical problems and make decisions ii.
construct truth tables to determine when statements are equivalent jj.
construct truth tables to demonstrate symbolic arguments and determine logical conclusions kk.
compose equivalent statements using logical techniques
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ll.
construct Euler Diagrams to demonstrate syllogistic arguments
7. Recommended Course Content and Approximate Time Spent on Each Topic
Linked to #6. Specific Course Objectives, Competencies, and Student Learning
Outcomes.
1 week Introduction to the course syllabus including a discussion of what will be expected throughout the semester
Invest $100,000 in the stock market
Review of Percents, simple interest and amortization schedules
(a,b,e,f)
1 -2 weeks Compound interest
Installment buying, including use of APR tables
(d,g,h)
1 -2 weeks Buying a house
(i,j,k)
1 week Annuities and loan formulas - take home exam
(i,j,k)
1 week Inductive reasoning
Estimation
Problem Solving
(l,m,n,o,p)
2 weeks Sampling techniques
Misuses of statistics
Frequency distributions
Statistical graphs
Measures of Central Tendency
Measures of Dispersion
The Normal Curve
(c,r,s,t,u,v,w,x)
4 weeks The nature of probability
Theoretical probability
Expected value
Tree diagrams and sample spaces
"Or" and "And" problems
Conditional probability
Counting principle and permutations
Combinations
Solving counting and probability problems using combinations
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(q,y,z,aa,bb,cc,dd,ee)
1-2 weeks Set concepts
Subsets
Venn diagrams and set operations
Venn diagrams and verification of equality
Application of sets
(ff,gg,hh)
2-3 weeks Statements and logical connectives
Truth tables for negation, conjunction, disjunction, conditional and biconditional
Equivalent statements
Symbolic arguments
Euler diagrams and syllogistic arguments
(ff,gg,hh,ii,jj,kk,ll)
8.
Text and Materials, Reference Materials, Auxiliary Materials and Content
Appropriate text(s) and materials will be chosen at the time the course is offered.
Examples include but are not limited to
Angel, Porter. Survey of Mathematics with Applications
Blitzer.
Smith.
Thinking Mathematically
Miller, Heeren, Hornsby. Mathematical Ideas
The Nature of Mathematics
Internet searches
9.
Recommended Course Requirements and Evaluation
Specific course requirements are at the discretion of the instructor at the time the course is being offered.
55%-90% Written - inclass exams
5%- 25% Out of class work (including take home exams and homework)
10%-25% Written reflective papers
10.
Methods of Instruction
Instructional methods will vary considerably with instructors. Specific methods will be at the discretion of the instructor teaching the course and the method by which the course is taught. These might include but are not limited to
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a.
exams and papers with feedback and discussion b.
lectures and class discussion c.
problem solving d.
Power Point presentations e.
videos, DVDs, CD-ROMs with detailed viewing guide and discussion questions f.
group activities g.
oral reports and other student presentations h.
games and simulations i.
web-based assignments and activities j.
reflective journals or papers k.
group and/or individual research projects with reports or poster presentations l.
study logs and study groups m.
other contemporary learning techniques (such as problem-based learning, investigative case-based learning) n.
homework assignments
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