Honors Finite Mathematics / Brief Calculus Class Description

Rio Salado MAT217 Finite Mathematics Syllabus: MAT217 Syllabus
Rio Salado MAT212 Brief Calculus Syllabus: MAT212 Syllabus

Honors Finite Mathematics (1st semester) is the Rio Salado college math course MAT217 Finite Mathematics for Business Analysis. From the Rio Salado course description: This course provides an introduction to the mathematics required for the study of business. It includes multivariable optimization, linear programming, linear algebra, probability, random variables, and discrete and continuous distributions.

The course consists of three general sections:

1) Optimization Problems: The first section's goal is for students to learn how to use mathematics to solve problems involving making optimum choices (maximizing profit, minimizing cost, etc.) Much of this section is review (equations of lines, solving systems of equations, solving systems of inequalities (2 variables only) using graphing) and after reviewing these foundations, the course emphasizes the ability to translate real-world situations into systems which can be solved, and then presents the Simplex Method for solving linear programming optimization problems in more than 2 variables.

2) Probability and Statistics: The second section is focused on developing an in-depth understanding of probability and how it informs decisions in real-world situations. This section begins with a review of set theory and extension with some new set concepts, reviews combinatorics (counting problems) and reviews and extends probability with more emphasis on conditional probability, Baye's theorem, binomial probability models, and expected value. It then examines ways of representing data graphically and provides a more rigorous treatment of statistics ideas such as mean, standard deviation and the normal distribution curve.

3) Review of precalculus (honors algebra 3-4) and introduction of limits: The last section in the semester is a review of the more important precalculus topics from honors algebra 3-4 and the introduction of the concept and rules of limits in preparation for brief calculus next semester.

Honors Brief Calculus (2nd semester) is the Rio Salado college math course MAT212 Brief Calculus. From the Rio Salado course description: This course provides an introduction to theory, techniques, and applications of the differential and integral calculus of functions with problems related to business, life, and the social sciences. The course includes the following topics:

1) Limits: Introduction to the idea of a limit and various methods of determining limits.

2) The derivative: Introduction to differential calculus including definition of derivative/instantaneous rate of change, methods of computing derivatives (including product/quotient rules, chain rule and implicit differentiation).

3) Applications of derivatives: Solving problems using derivatives including: curve sketching/asymptotes, velocity and acceleration, optimization and related rates problems.

4) The integral/antiderivatives: Introduction to integral calculus including the Fundamental Theorem of Calculus, area under a curve as Riemann Sum and as definite integral, and methods of computing antiderivatives including integration by substitution and integration by parts.

5) Applications of integrals: Solving problems using integrals including: volumes of solids of revolution, area under/between curves, function average value, probability density functions (and comparison with discrete Poisson probability models).

6) Introduction to multivariate calculus: A brief introduction to the concepts and procedures of calculus in 3 or more dimensions, including: graphing 3D functions, partial derivatives, 3D extrema and saddle points, and optimization problems using Lagrange multipliers.

Brief Calculus presents a coverage of many of the differential and integral calculus concepts covered in AP Calculus BC, but with an emphasis on conceptual understanding and application, rather than the very rigorous, detailed, and more theoretical approach found in most AP Calculus BC courses.

For some college majors, Finite Mathematics for Business Analysis and Brief Calculus are the most advanced math courses required. It is possible that students who are majoring in, for example, business, finance, or related fields may completely fulfill their college major math requirements by taking this class. For students who plan to major in fields such as engineering, chemistry, physics, meteorology, secondary education for mathematics, mathematics or statistics who will need to take Calculus I, Calculus II, Calculus III or further math courses, honors finite math/brief calculus will provide an excellent foundation for achievement in the more detailed calculus courses taken later, either at DV or in college.

Because this is a college math course, I have very high expectations for students. Don't be discouraged, though - if you were approved to take this class, then you can definitely handle the information and workload. It is important, however, to keep a few ideas in mind for success:

A good work ethic: You need to be willing to spend some time on homework for this class, and to fully engage during class time. Complete each and every assignment to the best of your ability. Remember, your achievement is directly related to your own effort!
Being prepared: Bring all materials needed, including your homework, class notes, a pencil and calculator to class every day.
Do not get behind: If you are having trouble, ask someone for help, either your teacher, a classmate, or someone at home. Take advantage of the free math tutoring provided in the classroom or the math office before/after school every school day. Make sure and do all the homework when it is first assigned, and ask questions when you don't understand in class or during tutoring.

Honors Finite Math / Brief Calculus is an interesting and useful class! I look forward to introducing you to these fascinating mathematical topics!