I. General Information
1. Course Title:
Mathematical Reasoning
2. Course Prefix & Number:
MATH 1442
3. Course Credits and Contact Hours:
Credits: 3
Lecture Hours: 3
4. Course Description:
This is a college level math course that satisfies MN Transfer Curriculum Goals 2 and 4 and is intended to increase students' problem-solving and mathematical reasoning skills. Topics include geometry, right triangle trigonometry, set theory, probability, statistics, and finance. Solving real world applications problems in each of these areas and communicating mathematically will be emphasized.
5. Placement Tests Required:
| Accuplacer (specify test): |
Math Introductory College Level or Algebra College Level or Pre-Calculus College Level or Calculus College Level |
Score: |
|
| Other (specify test): |
NGA AAF |
Score: |
236
|
6. Prerequisite Courses:
MATH 1442 - Mathematical Reasoning
There are no prerequisites for this course.
8. Prerequisite (Entry) Skills:
Fundamental algebra background and familiarity with a graphing calculator
9. Co-requisite Courses:
MATH 1442 - Mathematical Reasoning
There are no corequisites for this course.
II. Transfer and Articulation
1. Course Equivalency - similar course from other regional institutions:
Alexandria Technical & Community College, MATH 1415 Mathematical Reasoning, 3 credits
Itasca Community College, MATH 1101 Contemporary Mathematics, 3 credits
Lake Superior College, MATH 1105, Mathematical Reasoning, 3 credits
St. Cloud Technical & Community College, MATH 1331, Applications of Mathematical Reasoning, 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 2 – Critical Thinking
- 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 |
Justify the steps used in solving a mathematical problem. |
| Apply abstract ideas to concrete situations |
Apply appropriate mathematical formulas to solve problems in geometry, set theory, probability, statistics, and finance. |
| Utilize appropriate technology |
Utilize technology to solve mathematical application problems. |
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 (Goal 4);
- Apply logic in analyzing arguments (Goals 2 & 4);
- Apply higher-order problem-solving strategies (Goals 2 & 4);
- Solve applied financial problems involving simple and compound interest, annuities, and loans (Goal 4);
- Solve real-world problems that can be modeled with sets, permutations, and combinations (Goal 4);
- Display data graphically, calculate and interpret descriptive statistics, and assess possible bias in statistics (Goals 2 & 4);
- Apply the rules of probability in calculating expected values and conditional probabilities ( Goal 4);
- Solve real-world problems using two- and three-dimensional geometry (Goal 4); and
- Solve application problems that can be modeled by right triangles and solved using right triangle trigonometry (Goal 4).
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
- Sets and Counting
- Intersection, union, complement of sets
- Cardinal number formulas for union and complement
- Venn diagrams
- The Fundamental Theorem of Counting
- Permutations
- Combinations
- Using the correct counting principle for a given situation
- DeMorgan’s laws
- Probability
- The history of the development of probability theory
- The 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 probabilities and the product rule
- Punnett squares and basic probability in genetics
- Independence of events
- Statistics
- Frequency distributions and histograms
- Measures of central tendency for raw data and grouped data
- Range and 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.
- Finance
- Terminology of finance: principal, simple and compound interest, future value, present value, annuity, amortization, etc.
- Simple and compound interest formulas
- Credit card finance charges, bank deposits, and loans
- Ordinary annuities and annuities due
- Payout annuities
- Simple interest amortized loan formula, payment amounts, amortization schedules
- Geometry
- Perimeter and circumference of two-dimensional figures
- 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
- Basic two-column proofs
- Fibonacci numbers and the golden ratio
- Similar triangles and their applications
- Identification of conic sections by their graphs
- Reflective properties of parabolas, ellipses, and hyperbolas
- Center and radius of a circle from its equation
- Arcs of circles
- Trigonometric ratios of 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
- Using inverse trigonometric functions to find angles
- Applications of right triangle trigonometry