### Survey of College Mathematics

#### Welcome to Students

- What does this math course have to offer?
- This course fulfils a general education math foundation requirement by introducing linear equations, matrix algebra, Markov chains, linear programming, probability, data analysis, and the mathematics of finance. The applications are primarily from business, economics, and the life sciences. Throughout the course you'll be asked to develop, analyze, and interpret mathematical models, communicating your work in writing and in oral presentations in front of your peers.
- What are some skills that I can take from this class?
- Enumerating all the possible outcomes in a discrete probability space.
- Setting up a system of linear inequalities to model constraints.
- Constructing an annuity table for paying off a fixed-duration loan.

- What do I need to succeed in this class?
- Active, productive participation in each class and respect for the learning environment are expected of everyone. Leave your cell phone and similar electronic devices in the off mode or at home. Always read the textbook section that goes with the topic of the class. After reading one of the worked-out examples, test yourself using a similar problem from the exercises accompanying that section. Record your work in a separate math notebook, so that the tutors and your instructor can identify your strengths and weaknesses at a glance.
- Can you give me some examples of artifacts and reflections for an ePortfolio?
- Sure. Here are a few ideas from previous semesters:

#### Notes for Teachers

- What are some sections that take more time to cover than you first expected?
- Gauss-Jordan elimination
- Systems of linear inequalities (paradoxically, the shortcuts for solving a 2x2 system seems less easily retrievable after we've had a test on matrix methods than in the days leading up to that test)
- Binomial distributions and normal distributions

- What are some sections that take less time to cover than you first expected?
- Translating between matrix equations and linear systems
- Odds and independence

- Why jump straight to Markov chains before introducing probability?
- The linear evolution equations and the search for stationary state matrices offer real-world contexts for the operations of matrix multiplication and row reduction of augmented matrices, respectively, so that these operations are reinforced and less likely to be forgotten after the first test. In addition, students don't need the measure-theoretic baggage of probability definitions in order to reason about an entire population and its internal changes from one moment to the next. The empirical notion of probability in terms of fractions of a population is intuitive enough that students should have no trouble writing the discrete-time evolution equations from a verbal description. In the case of a population whose size is not fixed, linear evolution equations might still apply even when the language of probability does not, and the resulting extension of Markov chains offers rich possibilities for independent work by curious students. For everyone else, the early exposure to probability trees at this stage makes it easier to use these visual aids when discussing Bayes' formula.