This course consists of in-class lectures each week, and roughly biweekly asynchronous tutorials. Typically, the problems solved in high school are done mechanically or by mimicking solutions to similar problems in the textbook. In this course, you will develop the confidence and ability to approach and solve richer and more demanding problems.
Active participation in the lectures and tutorials and completion of the assigned homework are expected of all students.
By the end of this course, you should be able to:
- Sketch a picture of a Riemann Sum.
- Construct a Riemann sum to approximate the area under a curve and calculate it, by hand and by using a computational engine, and thereby answer questions in various contexts.
- Communicate in written form and in a mathematically precise way the concept of integration.
- Apply integration to find the area between curves and the average value of a function.
- Use the substitution rule to find the integral of a function.
- Use integration by parts to find the integral of a function.
- Represent probability scenarios via sketches of Venn Diagrams.
- Apply probability rules and concepts, such as conditional probability, dependence, multiplication rule, law of total probability, and Bayes Rule, to solve probability scenarios.
- Classify random variables and compute their mean and variance.
- Draw and interpret histograms, probability density functions, and cumulative probability functions.
