Welcome to Math 135: Topics in Contemporary Math!

Welcome to the first night of class! We're excited to embark on this mathematical journey with you. This course, Topics in Contemporary Math (MAT135), is designed to expose you to mathematical concepts that are both useful and relevant in today's world. You'll learn how to apply these ideas within a social context, making math more than just numbers on a page. Get ready to think critically and see the world through a mathematical lens!

Course Information

  • Course: MAT135 - Topics in Contemporary Math
  • Time: Monday 6:00pm - 8:45pm
  • Room: D222
  • Instructor: Tony Baker
  • Office Hours: Monday 5:00pm - 6:00pm (Appointment Only)
  • Contact: Padrick77@gmail.com, bakersmathclass.com

Syllabus Highlights

Here's a quick overview of what to expect this semester, as outlined in the syllabus:

  • Required Text: Quantitative Literacy: Thinking Between the Lines (Crauder, 2012)
  • Grading:
    • Participation and Attendance (15%)
    • Section Quizzes (60%) - Online, due one week after assignment.
    • Final Exam (25%) - Real-Life Application Project and Presentation
  • Attendance: Regular attendance and punctuality are expected.

Tonight's Class: Sections 1-1 and 1-5

Tonight, we'll be diving into sections 1-1 and 1-5. Make sure to review the PowerPoints and complete the online quizzes associated with these sections. Here's a sneak peek at what we'll be covering:

Section 1-1: Public Policy and Simpson's Paradox

We'll be exploring critical thinking and how averages can sometimes be misleading. A key concept is Simpson's Paradox, which occurs when:

  1. Combining or aggregating data masks underlying patterns.
  2. A factor distorts the overall picture, but the distortion goes away when underlying data are examined.

For example, we might look at a scenario where a school appears to perform worse than the state average, but when you break down the data by income level, the school actually outperforms the state in each category! This can be quite counterintuitive.

Let's consider how to calculate percentages, a fundamental skill in critical thinking. To find P% of a quantity, we use the formula:

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

For instance, if we want to find 45% of 500, we calculate:

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

Section 1-5: Critical Thinking and Number Sense

In this section, we'll focus on developing your number sense and how to cope with the myriad measurements encountered daily. We will cover magnitudes and powers of 10. For example:

  • $10^3 = 1,000$ (thousand)
  • $10^6 = 1,000,000$ (million)
  • $10^{-2} = 0.01$ (hundredth)
  • $10^{-3} = 0.001$ (thousandth)

We will also work with exponents.

Negative exponents are defined as: $a^{-n} = \frac{1}{a^n}$. So for example, $10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001$.

And zero exponents are defined as: $a^0 = 1$.

We will also cover the basic properties of exponents like, $a^p a^q = a^{p+q}$, $\frac{a^p}{a^q} = a^{p-q}$, and $(a^p)^q = a^{p*q}$.

We'll also discuss the importance of estimation and using critical thinking to make informed decisions when comparing costs and values. For instance, when comparing prices in different units (like square feet vs. square yards), understanding the relationships between these units is crucial.

Get Ready to Learn!

We're looking forward to a great semester of exploring the world through the lens of mathematics. Come prepared to participate, ask questions, and think critically! See you in class!