MATH 1030 - Mathematics for the Liberal Arts

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 posed.

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