I. General Information

1. Course Title:
Concepts in Mathematics

2. Course Prefix & Number:
MATH 1441

3. Course Credits and Contact Hours:

Credits: 3

Lecture Hours: 3

4. Course Description:

This is a college level math course that demands a fundamental algebra background and familiarity with a calculator. Topics include at least four of the following: geometry, trigonometry, graphs, logic, probability, statistics, finance, numeration systems, and set theory.

5. Placement Tests Required:

Accuplacer (specify test):

College Level Math

Score:

50

6. Prerequisite Courses:

8. Prerequisite (Entry) Skills:
Fundamental algebra background and familiarity with a calculator.

9. Co-requisite Courses:

There are no corequisites for this course.

II. Transfer and Articulation

1. Course Equivalency - similar course from other regional institutions:

St. Cloud State University, MATH 105 Culture of Mathematics, 3 credits
Itasca Community College, MATH 1101 Contemporary Mathematics, 3 credits

III. Course Purpose

2. MN Transfer Curriculum (General Education) Courses - This course fulfills the following goal area(s) of the MN Transfer Curriculum:
Goal 4 – Mathematical/Logical Reasoning

IV. Learning Outcomes

1. College-Wide Outcomes

College-Wide Outcomes/Competencies	Students will be able to:
Analyze and follow a sequence of operations	Explain what constitutes a valid mathematical argument
Apply abstract ideas to concrete situations	Clearly express mathematical/logical ideas in writing

2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of the course:

• Clearly express mathematical ideas in writing.  MnTC Goal 4
• Understand probability and statistics.  MnTC Goal 4
• Apply higher-order problem-solving strategies.  MnTC Goal 4
• Solve applied financial problems.  MnTC Goal 4
• Clearly express mathematical ideas in writing.  MnTC Goal 4
• Illustrate historical and contemporary applications of mathematical/logical systems.  MnTC Goal 4
• Understand the fundamentals of logic.  MnTC Goal 4
• Understand the fundamentals of sets and notation.  MnTC Goal 4
• Understand the fundamentals of algebra, graphs, and functions.  MnTC Goal 4
• Solve systems of linear equations and inequalities.  MnTC Goal 4
• Illustrate historical and contemporary applications of mathematical/logical systems.  MnTC Goal 4

V. Topical Outline

Listed below are major areas of content typically covered in this course.

1. Lecture Sessions

At least four of the following topics will be covered.

1. Logic
• Statements
• Truth Tables
• Conditional and Biconditional
• Variations of the Conditional and Implications
• Euler Diagrams
• Truth Tables and Validity
• Switching Networks
2. Sets and Counting
• Cardinal number formulas for union and complement
• Venn diagrams
• DeMorgan’s Laws
• Fundamental Theorem of Countin
• Permutations
• Combinations
• Determining the correct counting principle for a given situation
• Intersection, union, complement of sets
3. Probability
• Understand the history of the development of probability theory.
• Terminology of probability:experiment, sample space, event, outcome, relative frequency, odds.
• Basic rules of probability
• Using counting principles (permutations, combinations) to calculate probabilities
• Expected value
• Conditional probability and the product rule
• Punnett squares 
• Independence of events
4. Statistics
• Frequency distributions and histograms
• Measures of central tendency for raw data and grouped data
• Standard deviation for a set of raw data and for grouped data
• The standard normal (z-) distribution
• Margin of error and level of confidence 
• Terminology of statistics: population, sample, data, frequency distribution, histogram, measures of central tendency, measures of dispersion, et
5. Finance
• Terminology of finance: principal, simple and compound interest, future value, present value, annuity, amortization, etc.
• Using the compound interest formula
• Credit card finance charges, bank deposits and loans
• Ordinary annuities and annuities due
• Using the simple interest formula
• Payout annuities
• Simple interest amortized loan formula, payment amounts, amortization schedules
6. Geometry
• Perimeter and circumference
• Area formulas for triangles, rectangles, trapezoids, parallelograms and circles.
• Volume and surface area of rectangular prisms, cylinders, cones, pyramids, and spheres
• The use of geometry in one or more ancient civilizations
• Understand and develop basic two-column proofs
• Similar triangles and their applications
• Conic sections—graphs and equations
• The focus and directrix of a parabola
• Foci of ellipses and hyperbolas
• Center and radius of a circle from its equation
7. Trigonometry
• Trigonometric ratios of sine, cosine, and tangent for right triangles
• Sine, cosine, and tangent for acute angles of a right triangle
• Sine, cosine, and tangent for the special angles (30, 45, 60 degrees) of a right triangle
• Acute angles from inverse trig ratios and their applications
• Use of a scientific calculator to determine sine, cosine, and tangent for any angle
8. Graph Theory
• Konigsberg Bridge Problem
• Graphs and Euler Trails
• Hamilton Circuits
• Networks
• Scheduling
9. Numeration Systems
• Place Systems
• Arithmetic in Different Bases
• Prime Numbers and Perfect Numbers
• Fibonacci Numbers and the Golden Ratio