Welcome to Math Class!
Welcome to MAT135 - Topics in Contemporary Math! This website will serve as the central hub for all class materials, including notes, assignments, and important announcements. Our goal is to create a supportive and engaging learning environment where you can develop your mathematical skills and confidence.
New notes and assignments will be posted at midnight on the day of each class. We encourage you to review the material beforehand so you can come to class prepared with specific questions. This will help us make the most of our time together!
Here are the resources for our first day:
- Class Syllabus - Please review this document carefully as it outlines the course policies, grading breakdown, and important dates.
- Notes For Section 1-1 - These are the notes we'll be covering in class today.
- Section 1-1 Assignment - This is the homework assignment due next class.
Key Concepts from Section 1-1: Critical Thinking
Our first section focuses on Critical Thinking, a fundamental skill applicable far beyond the realm of mathematics. We'll be exploring how to analyze information, identify potential biases, and draw sound conclusions. One of the key concepts we'll introduce is Simpson's Paradox.
Simpson's Paradox, as shown in the notes, is a statistical phenomenon where a trend appears in several different groups of data but disappears or reverses when these groups are combined. This highlights the importance of looking beyond simple averages and considering underlying factors. Consider the following example:
Suppose a certain high school gave a math proficiency exam to its students and the percentage who passed was below the statewide average. After examining the figures further, the school decided to report its test data by separating them into students from low-income families and students from higher-income families.
| Local School | Statewide | |||
|---|---|---|---|---|
| Students Tested | Passed | Students Tested | Passed | |
| Low Income | 400 | 260 | 200,000 | 128,000 |
| High Income | 700 | 532 | 1,100,000 | 825,000 |
| Total | 1100 | 792 | 1,300,000 | 953,000 |
The notes provide an example: Separating test scores by the economic level of the students may show that at a local school students at each economic level perform better than the statewide average for students at the same level. But, if school has more students at lower economic levels, its test scores overall may be lower than the state average. Such results can be counterintuitive. Without careful consideration, one can be led to an incorrect conclusion.
Another example covered in the notes is The Berkeley gender discrimination case. Data from a 1973 study showed persuasive evidence that the University of California at Berkeley was practicing gender discrimination in graduate school admissions.
Key Formulas
Here are a few formulas that might be useful for this section:
- To calculate P% of a quantity, we multiply the quantity by $\frac{P}{100}$: $$P\% \text{ of quantity} = \frac{P}{100} \times \text{Quantity}$$
- To find what percentage of a whole is a part: $$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\%$$
Contact Information
If you have any questions, please don't hesitate to contact me by email (Padrick77@gmail.com). You can also leave a comment on this post or any other post on the website – your classmates are a great resource too!
I'm looking forward to a great semester with all of you!