## 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:

MATH 1441 - Concepts in Mathematics

Applies to all requirements

Accuplacer College Level Math score of 50 or higher, or MATH 1505 or MATH 1506

8. Prerequisite (Entry) Skills:

Fundamental algebra background and familiarity with a calculator.

9. Co-requisite Courses:

MATH 1441 - Concepts in Mathematics

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

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: |

Assess alternative solutions to a problem |
Apply higher-order problem-solving and/or modeling strategies. |

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.

- Logic
- Statements
- Truth Tables
- Conditional and Biconditional
- Variations of the Conditional and Implications
- Euler Diagrams
- Truth Tables and Validity
- Switching Networks

- 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

- 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

- 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

- 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

- 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

- 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

- Graph Theory
- Konigsberg Bridge Problem
- Graphs and Euler Trails
- Hamilton Circuits
- Networks
- Scheduling

- Numeration Systems
- Place Systems
- Arithmetic in Different Bases
- Prime Numbers and Perfect Numbers
- Fibonacci Numbers and the Golden Ratio

## 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:

MATH 1441 - Concepts in Mathematics

Applies to all requirements

Accuplacer College Level Math score of 50 or higher, or MATH 1505 or MATH 1506

8. Prerequisite (Entry) Skills:

Fundamental algebra background and familiarity with a calculator.

9. Co-requisite Courses:

MATH 1441 - Concepts in Mathematics

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.

- Logic
- Statements
- Truth Tables
- Conditional and Biconditional
- Variations of the Conditional and Implications
- Euler Diagrams
- Truth Tables and Validity
- Switching Networks

- 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

- 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

- 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

- 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

- 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

- 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

- Graph Theory
- Konigsberg Bridge Problem
- Graphs and Euler Trails
- Hamilton Circuits
- Networks
- Scheduling

- Numeration Systems
- Place Systems
- Arithmetic in Different Bases
- Prime Numbers and Perfect Numbers
- Fibonacci Numbers and the Golden Ratio