MA 101

Modern College Mathematics I

Since this is a liberal arts mathematics course whose purpose is to expose students to a variety of mathematical topics that are of current interest, not all topics listed below can be covered in a one-semester course. Typically, three of the major topics listed below are the focus of a course. Topics are chosen by the individual instructor. Each learning outcome corresponds with one major topic.

    1. Sets
      a) Basic concepts
      b) Venn diagrams and subsets
      c) Set operations
      d) Infinite sets, cardinal numbers, countability and uncountability 

    2. Logic
      a) Statements
      b) Truth tables / Equivalent statements
      c) Euler diagrams
      d) Analysis of arguments
      e) Applications: Computer circuits

    3. Numeration and Mathematical Systems, Number Theory 
      a) Historical numeration systems
      b) Arithmetic in the Hindu-Arabic system
      c) Converting between number bases
      d) Clock arithmetic and modular systems
      e) Other finite mathematical systems
      f) Groups
      g) Prime and composite numbers
      h) Greatest common divisor and least common multiple
      i) Perfect numbers
      j) Sequences
      k) Fibonacci numbers
      l) Golden ratio
      m) Solved and unsolved problems in number theory

    4. Fundamental Counting Principle
      a) Permutations
      b) Combinations
      c) Fundamental Counting Principle
      d) Applications to Probability

    5. Voting and Apportionment
      a) Plurality Method
      b) Pairwise Comparison Method
      c) Borda Method
      d) Condercet Criterion
      e) Benefits and shortcomings of each method
      f) Applications

    6. GraphTheory
      a) Walks, paths, and circuits
      b) Colorability
      c) Euler Circuits
      d) Hamiltonian Circuits
      e) Trees

    7. Personal Financial Management
      a) Time value of money
      b) Consumer credit
      c) Truth in lending
      d) Costs and advantages of home ownership
      e) Financial investments

Learning Outcome 1: The student will have demonstrated the knowledge and use of applications of set concepts.

Learning Outcome 2: The student will have demonstrated the knowledge and use of applications of basic logic.

Learning Outcome 3: The student will have demonstrated an understanding of mathematical systems and their properties.

Learning Outcome 4: The student will have demonstrated the comprehension of the Fundamental Counting Principle as applied to the area of probability and its applications.

Learning Outcome 5: The student will demonstrate knowledge of the major voting and apportionment methods.

Learning Outcome 6: The student will have demonstrated an understanding of basic graph theory.

Learning Outcome 7: The student will have demonstrated knowledge of the fundamental principles and real-world applications of personal financial management.