MTH4419 CONTEMPORARY MATHEMATICS
3 Credit Hour
Student Level: This course is open to students on the college level in either the freshman or sophomore year.
MTH4419 - Contemporary Mathematics (3 hrs)
The mathematics of problem solving, geometry of shapes, number systems, statistics, functions and set theory. Note: This will not satisfy courses specifically designating college Algebra as a prerequisite.
Course Classification: Lecture
Prerequisites: Minimum grade of C in MTH 4410 Intermediate Algebra or the equivalent, or placed based on mathematics course placement guidelines.
Controlling Purpose: This course is designed to meet the needs of students majoring in nontechnical degree programs that do not require courses for which college algebra is a prerequisite, and for students who wish to survey some practical applications of mathematics to non-technical or nonSTEM fields.
Learner Outcomes: Upon completion of this course, the student will gain understanding of mathematics and problem solving. This course covers topics such as decision-making, geometry of shapes, statistics, functions and graphs, set theory and numerical systems. Prepares students for the mathematics encountered in other college courses that use quantitative reasoning. Emphasis on developing critical thinking and quantitative reasoning skills needed to understand major issues in society.
UNIT 1: Thinking Critically
Outcomes: The student will learn critical thinking skills
- Identify an argument’s premises and conclusions.
- Recognize fallacious arguments, which contain logical flaws.
- Evaluate media information using a five step method
- Distinguish between truth tables for negation, conjunction, disjunction, and conditional
- Distinguish the difference between inclusion or exclusive “or”.
- Identify the variations on the conditional including the converse, inverse and contrapositive.
- Identify set relationships such as subsets, disjoint sets, and overlapping sets.
- Describe the four standard categorical propositions.
- Apply Venn diagrams to illustrate set relationships and organize information.
- Evaluate inductive arguments in terms of strength.
- Evaluate deductive arguments in terms of validity and soundness.
- Evaluate Venn diagram tests of validity.
- Evaluate chains of conditionals.
- Propose a theorem inductively.
- Prove a theorem inductively.
- Apply the seven steps for critical thinking.
UNIT 2: Approaches to Problem Solving
Outcomes: The student will be able to problem solve using units and know problems solving guidelines and hints.
- Explain the key words per, of, square, cube and a hyphen.
- Write conversion factors in three equivalent forms.
- Explain that unit conversions mean multiplying by 1.
- Convert basic USCS and metric units.
- Identify metric prefixes.
- Distinguish between temperature units and convert between ˚F, ˚C, and Kelvin.
- Work with units to check answers and help solve problems.
- Identify energy units and power units.
- Apply the concept of density to materials, population, and information.
- Apply the concept of concentration to medical dosage problems, air and water pollution, and blood alcohol content.
- Apply the four- step problem solving process
- Apply the eight hints for problem solving.
UNIT 3: Numbers in the Real World
Outcomes: The student will be able to apply numbers to real-world contexts to solve problems
- Find absolute change, relative change, absolute difference, and relative difference.
- Explain the difference between the “of” versus “more than” rule.
- Explain the difference between percentage points versus %.
- Solve percentage problems.
- Identify common abuses of percentages.
- Write and interpret numbers in scientific notation.
- Put numbers in perspective.
- Distinguish significant digits from non-significant zeros.
- Identify and distinguish between random and systematic errors.
- Find absolute error and relative error.
- Distinguish between accuracy and precision.
- Apply rounding rules for combining approximate numbers.
- Describe index numbers and how they are useful for comparisons.
- Find index number.
- Explain how the CPI is used to measure inflation.
- Adjust prices for inflation with the CPI.
UNIT 4: Managing Money
Outcomes: The student will know the basics for managing money.
- Explain the importance of controlling your finances.
- Demonstrate how to make a budget.
- Identify factors that determine whether your spending patterns make sense for your situation.
- Apply the various compound interest formulas.
- Explain investment types: stock, bond, and cash.
- Interpret financial tables for stocks, bonds, and mutual funds.
- Utilize important principles of investing.
- Identify the uses and dangers of credit cards.
- Explain strategies for early payment of loans.
- Explain considerations in choosing a mortgage.
- Define different types of income as they apply to taxes.
- Apply tax rate tables to calculate taxes.
- Distinguish between tax credits and tax deductions.
- Calculate FICA taxes.
- Identify special tax rates for dividends and capital gains.
- Explain the benefits of tax-deferred savings plans.
- Distinguish between a deficit and a debt.
- Explain basic principles of the federal budget.
- Distinguish between publicly held debt and gross debt.
- Identify major issues concerning the future of Social Security.
UNIT 5: Statistical Reasoning
Outcomes: The student will know the fundamentals of statistics and be able to judge the reliability of a statistical study.
- Identify and interpret the five basic steps in a statistical study and the importance of a representative sample.
- Explain the four common sampling methods.
- Distinguish between observational studies and experiments.
- Explain the placebo effect and the importance of blinding in experiments.
- Find a confidence interval from a margin of error.
- Apply eight guidelines for evaluating a statistical study.
- Interpret multiple bar graphs, stack plots, contour maps and other media graphs.
- Distinguish between true three-dimensional data and graphs that have a three-dimensional look for cosmetic reasons only.
- Identify and explain the common cautions about graphs.
- Distinguish between correlation and causality.
- Create and interpret scatterplots.
- Explain three possible explanations for a correlation.
- Apply six guidelines for establishing causality.
UNIT 11: Mathematics and the Arts
Outcomes: Students will understand how mathematics can be used in the various arts.
- Identify how a plucked string produces sound.
- Measure frequency in cycles per second, and find harmonics of the frequency.
- Identify the musical scale and the ratios of frequencies among musical notes.
- Explain the difference between analog and digital representation of music.
- Explain the use of perspective in painting.
- Find the symmetries in paintings and tilings.
- Create tilings with regular or irregular polygons.
- Explain and solve questions about the golden ratio and Fibonacci sequence.
- Explain the claimed uses of golden ratio in both art and nature.
UNIT 12: Mathematics and Politics
Outcomes: The student will understand the basics of how mathematics is used in politics.
- Describe the mathematics involved in electing the U.S. president, including primaries, general election and Electoral College.
- Identify variations on majority rule.
- Apply five methods for deciding an election with three or more candidates.
- Apply the four fairness criteria.
- Explain why no voting method can satisfy all fairness criteria in all cases.
- Explain approval voting as an alternative voting system.
- Explain variations in voting power when not all voters have equal weight.
- Describe the history of apportionment mathematics.
- Apply four apportionment methods.
- Identify the potential flaws of each method.
- Explain the significance of the Balinsky and Young theorem.
Projects Required: Instructor determined
Text Book: Contact the Bookstore for current textbook information.
References: None required.
Materials/Equipment Required: Scientific Calculator required, Graphing Calculator (TI-83, 83 Plus) recommended.
Attendance Policy: Students should adhere to the attendance discussed on the first day of class.
Grading Policy: Grading may vary according to the instructor.
Maximum class size: 25
Refer to the following policies:
402.00 Academic Code of Conduct
263.00 Student Appeal of Course Grades
403.00 Student Code of Conduct
Disability Services Program:
Cowley College, in recognition of state and federal laws, will accommodate a student with a documented disability. If a student has a disability, which may impact work in this class, which requires accommodations, contact the Disability Services Coordinator.