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:	35
Other (specify test):	Elementary Algebra	Score:	76

6. Prerequisite Courses:

7. Other Prerequisites
Math ACT score of 20

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	Express mathematical/logical ideas clearly in writing.

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

• Express mathematical ideas clearly in writing (MnTC Goal 4);
• Apply logic in analyzing arguments (MnTC Goal 4);
• Apply higher-order problem-solving strategies (MnTC Goal 4);
• Solve applied financial problems (MnTC Goal 4);
• Solve real-world problems that can be modeled with permutations and combinations (MnTC Goal 4);
• Calculate measures of center and measures of dispersion (MnTC Goal 4);
• Apply the rules of probability in calculating expected values and conditional probabilities (MnTC Goal 4);
• Solve application problems using systems of linear equations and inequalities (MnTC Goal 4);
• Solve real-world problems by calculating perimeters, areas, surface areas, and volumes (MnTC Goal 4); and
• Solve application problems that can be modeled by right triangles and solved using right triangle trigonometry (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 counting
• Permutations
• Combinations
• Determining the correct counting principle for a given situation
• Intersection, union, complement of sets
3. Probability
• 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, etc.
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