Welcome to MAT135!

Hello and welcome to MAT135: Topics in Contemporary Mathematics for the Spring of 2014! I'm excited to embark on this mathematical journey with you. This course will expose you to mathematics in a way that is both useable and relevant in today's world. We'll focus on applying mathematical ideas within a social context, enhancing your quantitative literacy and critical thinking skills.

Below, you'll find your course syllabus and assignments for today's class. Every class, a new post will appear here containing the day's notes and quizzes for each section. These posts will be available by midnight on the day of the class, allowing you to print out the notes and review the quizzes beforehand if you wish. All quizzes are to be completed via the links on this site and are due by the start of the next week's class. Be sure to seek assistance regularly if problems are not understood, keeping all work in a notebook that may be reviewed by the instructor at any time.

Course Information

  • Course: MAT135 – Topics in Contemporary Math
  • Time: Mondays 6:30pm - 9:15pm
  • Room: D222

Instructor Information

Course Syllabus

Make sure to review the syllabus, which outlines course expectations, grading, attendance, and other important policies. The syllabus emphasizes the importance of participation (35% of the final grade), section quizzes (40% of the final grade), and a final real-life application project and presentation (25% of the final grade).

Sections 1.1 and 1.2: Critical Thinking and Logic

Today, we'll be diving into Sections 1.1 and 1.2 from the textbook Quantitative Literacy: Thinking Between the Lines. These sections introduce the foundational concepts of critical thinking and logical fallacies, equipping you with the tools to analyze information and construct sound arguments.

Section 1.1: Public Policy and Simpson's Paradox

Section 1.1 explores a fascinating concept called Simpson's Paradox. This paradox highlights how aggregated data can sometimes mask underlying patterns, leading to potentially misleading conclusions. A key learning objective is to view conclusions based on averages with a critical eye. For example, we might see situations where a local school outperforms statewide averages in specific categories (e.g., low-income and high-income students), yet has a lower overall passing percentage.

Consider a situation where calculating percentages becomes important: To calculate $P\%$ of a quantity, we use the formula:

$$P\% \text{ of quantity} = \frac{P}{100} \times \text{Quantity}$$

For example, find $45\%$ of $500$:

$$45\% \text{ of } 500 = \frac{45}{100} \times 500 = 225$$

Section 1.2: Logic and Informal Fallacies

Section 1.2 delves into the realm of logic and informal fallacies. Logic is the study of methods and principles used to distinguish between good and bad reasoning. A logical argument consists of premises (hypotheses) and a conclusion. The argument is considered valid if the premises logically support the conclusion.

We'll also examine various informal fallacies. These are flaws in reasoning that arise from the content of an argument rather than its structure. Some examples include:

  • Appeal to Ignorance: Arguing that something is true because it hasn't been proven false (or vice versa).
  • Dismissal based on Personal Attack (Ad Hominem): Rejecting an argument based on the character of the person making it.
  • False Authority: Citing an authority who lacks expertise on the topic.
  • Straw Man: Misrepresenting an opponent's argument to make it easier to attack.

We will distinguish between deductive and inductive arguments. A deductive argument draws a specific conclusion from general premises (e.g., All men are mortal; Socrates is a man; Therefore, Socrates is mortal). An inductive argument draws a general conclusion from specific examples.

Assignments for Today

  • Review the Course Syllabus
  • Study Section 1-1 Notes
  • Complete Quiz 1-1
  • Study Section 1-2 Notes
  • Complete Quiz 1-2

I am looking forward to a great semester of learning and discovery! Let's work together to make this a successful and enjoyable experience for everyone.