Course Outline for Mathematics 33S
Finite Mathematics with Support

Effective: Fall 2019
SLO Rev: 09/09/2018
Catalog Description:

MTH 33S - Finite Mathematics with Support

4.50 Units

Straight lines, systems of linear equations, matrices, systems of linear inequalities, linear programming, mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to probability. Applications in business, economics and the social sciences. This course is equivalent to MTH 33 with additional lab hours for students who did not place directly into MTH 33 or for students who place directly into MTH 33 but desire additional instruction.
Prerequisite: MTH 55 or MTH 55B or an appropriate placement through the Mathematics Placement process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 4.00 72.00 144.00 216.00
Laboratory 0.50 36.00 0.00 36.00
Total 4.50 108.00 144.00 252.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. interpret graphs of linear equations;
  2. identify the three types of solutions of a linear system;
  3. use Gauss-Jordan elimination to put a matrix into reduced row echelon form;
  4. write a system of linear equations to solve an applied problem;
  5. perform operations with data matrices and interpret the result;
  6. solve a system of linear equations and interpret the result;
  7. find the inverse of a square matrix;
  8. use the inverse to solve a system of linear equations;
  9. determine graphically the solution of a system of linear inequalities;
  10. formulate the solution to a linear programming problem in two or three variables;
  11. use graphical methods to solve a linear programming problem in two variables;
  12. find unions, intersections and complements of sets;
  13. use Venn diagrams to solve problems;
  14. apply basic combinatorial principles to counting problems;
  15. demonstrate an understanding of the basic definitions of elementary probability;
  16. determine the probability of a simple or compound event using combinatorics and basic probability theorems;
  17. determine whether events are independent;
  18. use conditional probability to find the probability of compound events;
  19. use Bayes’ theorem to find probabilities;
  20. determine the probability distribution and expected value of a random variable;
  21. solve applied problems involving simple and compound interest;
  22. solve applied problems involving annuities, sinking funds and amortization;
  23. solve applications modeled with exponential and logarithmic functions;
  24. be able to use calculator and/or computer technology to solve complex finite math problems.
Course Content:
  1. Review of simplifying and evaluating algebraic expressions
    1. Order of operations
    2. Exponential expressions
    3. Logarithmic expression
  2. Review linear equations and functions, intersection of straight lines
    1. Graphing linear functions using intercepts and/or slope
    2. Finding linear equations from data
  3. Applications of linear functions to economics
    1. Cost, revenue and profit functions
    2. Supply and demand equations
    3. Break-even point
    4. Market equilibrium
  4. Review exponential exponential equations and functions
  5. Review logarithmic equations and functions
  6. Applications modeled with exponential and logarithmics functions
  7. Systems of linear equations
    1. Graphing , substitution and elimination
    2. Types of solutions, unique and non-unique solutions and inconsistent systems
    3. Applications to business and social science
  8. Matrices and Matrix methods for solving systems of equations
    1. Gauss-Jordan elimination and reduced-row echelon form 
    2. Matrix algebra
    3. Inverse matrix method for solving systems of linear equations
    4. Applications to business and social science
  9. Linear programming
    1. Graphical solution of a system of linear inequalities
    2. Formulation of a linear programming problems in two and three variables 
    3. Graphical solution methods of linear programming problems in two variables
    4. Applications to business and social science
  10. Math of finance
    1. Simple and compound interest
    2. Future amount and present value
    3. Annuities, sinking funds and amortization
  11. Sets and counting
    1. Subsets, set equality, union, intersection and complement
    2. Set builder notation and Venn diagrams
    3. DeMorgan’s Laws
    4. Counting elements in a set using Venn diagrams and/or formulas
    5. Multiplication rule 
    6. Permutations and combinations
    7. Applications to business and social science
  12. Probability
    1. Basic definitions, principles and theorems of probability theory
    2. Probability distributions and expected value
    3. Use of  combinatorial principles to determine the probability of an event
    4. Finding the probability of a compound event 
    5. Conditional probability
    6. Independence of two events
    7. Bayes' Theorem 
    8. Applications to business and social science
Lab:
  1. Applications
    1. Finance
    2. Linear functions
    3. Exponential functions
    4. Linear Programming
    5. Probability
  2. Use of technology
  3. Study Skills
    1. Grit and Growth Mindset
    2. How Learning Math is Different
    3. Resources On and Off Campus
    4. Time Management
    5. How to Be an Effective Listener and Take Notes
    6. How to Approach Homework
    7. How to Study for an Exam
    8. Overcoming Math and Test Anxiety
Methods of Instruction:
  1. Lecture/Discussion
  2. Problem Solving
  3. Group Activities
  4. Textbook reading assignments
Assignments and Methods of Evaluating Student Progress:
  1. A company makes widgets and gadgets. Widgets are comprised of 10 units canvas, 5 units nylon. Gadgets are comprised of 8 units canvas, 9 units nylon. The company has 1000 units of canvas and 800 units of nylon available. A widget returns $12 profit and a gadget returns $15 profit. How many widgets and how many gadgets should be manufactured to maximize profit?
  2. Using an interest rate of 7% per year, set up the formula to determine how much someone should pay now (the present value) for an annuity that would pay the purchaser $200 per month for the next 10 years.
  1. Exams/Tests
  2. Quizzes
  3. Projects
  4. Homework
  5. Final Examination
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Lial, M., R. Greenwell, N. Ritchey. (2016). Finite Mathematics (11th). Pearson.
  • Spreadsheet (e.g. Excel)
  • Grapher (e.g. www.desmos.com)
  • Computer algebra system (e.g. www.wolframalpha.com)
  • May require scientific or graphing calculator.
Abbreviated Class Schedule Description:
Straight lines, systems of linear equations, matrices, systems of linear inequalities, linear programming, mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to probability. Applications in business, economics and the social sciences. This course is equivalent to MTH 33 with additional lab hours for students who did not place directly into MTH 33 or for students who place directly into MTH 33 but desire additional instruction.
Prerequisite: MTH 55 or MTH 55B or an appropriate placement through the Mathematics Placement process.
Discipline:
Mathematics*