MATH 1030 - Mathematics for the Liberal Arts

Credits: 3
Hours/Week: Lecture 3 Lab None
Course Description: Designed for the liberal arts or humanities major whose program does not require statistics, college algebra, or precalculus, this course presents concepts and strategies not emphasized in traditional mathematics courses. Topics include problem-solving strategies; historical and contemporary number systems; mathematics in culture and society; cryptography; fractals; graph theory and optimal planning; growth models and finance; sets and set operations; and probability. Not intended as a prerequisite for other mathematics courses. Use of graphing technology, such as the TI-84, is required (see instructor for acceptable models).
MnTC Goals
4 Mathematics/Logical Reasoning

Prerequisite(s): Course placement into MATH 1030 or higher, or concurrently enrolled in MATH 0020 , or completion of MATH 0060  or MATH 0070  or MATH 1025  or above with a grade of C or higher.
Corequisite(s): None
Recommendation: Eligible for college-level Reading and English.

Major Content

1. Historical and contemporary counting systems
   1. Hindu-Arabic base-10 system
   2. Babylonian and Mayan place-value systems
   3. Contemporary number systems
      1. Binary
      2. Octal
      3. Hexadecimal 
   4. Conversions to and from base-10
2. Cryptography
   1. Simple shift ciphers
   2. Caesar cipher
   3. Modular arithmetic
      1. Operations
      2. Shift cipher formulas
3. Fractals
   1. Strictly self-similar fractals
      1. Cantor set
      2. Koch curve
      3. Sierpinski gasket
   2. Hausdorff dimension
   3. Mandelbrot set
      1. Complex numbers
      2. Recursive formula
4. Sets  
   1. Set notation
   2. Describing sets
   3. Set operations
      1. Union
      2. Intersection
      3. Complement
   4. Venn diagrams
5. Probability
   1. Counting
      1. Basic counting principles
      2. Permutations
      3. Combinations
   2. Probability of an event
   3. Probability rules for the set operations
   4. Venn diagrams and probability
6. Growth models and finance
   1. Growth models
      1. Linear
      2. Exponential
      3. Logistic
   2. Simple finance
      1. Simple interest
      2. Compound interest
      3. Continuous compound interest
   3. Consumer finance
      1. Annuities
      2. Loans
7. Graph theory and networks
   1. Components of a graph
   2. Types of graphs
   3. Graphs with weighted and unweighted edges
   4. Optimal planning
      1. Dijkstra’s algorithm for optimal path
      2. Sorted edges algorithm for Hamiltonian circuits
      3. Kruskal’s algorithm for minimum cost spanning tree
      4. Euler paths and circuits

1. perform independent investigations of mathematical ideas.
2. demonstrate critical and logical reasoning when solving problems.
3. describe how various mathematical ideas have developed over time.
4. describe the history of mathematics and the interaction between different cultures in relation to mathematics.
5. quantify concepts in the real-world using numbers.
6. apply mathematics to a changing world and everyday situations employing a diverse set of mathematical skills.
7. identify and justify observed patterns.
8. generate numeric, geometric, and algebraic patterns to demonstrate a variety of relationships.
9. apply a variety of computational procedures to examine the reasonableness of conjectures and solutions to problems.
10. represent mathematical information in symbolic, visual, numerical, verbal, and written forms.
11. discuss the relationship between mathematics and other fields.
12. integrate technological and nontechnological tools with mathematics.
13. communicate clearly a problem’s solution and its explanation for the intended audience in terms of the problem pose

04. 02. Clearly express mathematical/logical ideas in writing.

04. 03. Explain what constitutes a valid mathematical/logical argument(proof).

04. 04. Apply higher-order problem-solving and/or modeling strategies.

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