# Math 120: Introduction to Contemporary Mathematics (Spring, 2022)

#### Basic Information

• Dr. Manil Suri, suri@umbc.edu,
Office hours: MW 3:30-4:30 by appointment (please email!)
• Lectures: MW 5:30-6:45. These will be synchronously via Blackboard Collaborate until Spring Break, but in person after that. You will need to attend classes in person (in ITE 104) starting on Mar 28.
• Text: Math in Society edited by David Lippman, course reserves and online articles
• Required Technology: Class will be online until Spring Break, in-person afterwards. Webcam or other means to transmit image will be needed for online part.
• Prerequisites: Math 104, 106 or Grade 3,4,5 on LRC Math placement test.

#### Outline and Syllabus

The course is divided into three sections:

A. RATES AND GROWTH: An important part of mathematics is to be able to make calculations and predictions based on data and trends. In this section, we will explore such techniques, by reviewing and building upon material that you have seen before in earlier math classes. Particular attention will be paid to how math helps us understand the COVID pandemic. The sequence of connected topics we will cover is:

1. Percentages and Decimals: This will be mainly review – refer to pages 1-5 of “Problem Solving” chapter in textbook. Quiz-1 and Quiz0 will be based on this. We will also discuss this essay by J. Ellenberg about real-life examples where percentages have been used to generate fake news. One of the issues that will come up is how to round answers that are decimals. We will define absolute and relative change.
2. Linear Growth: Refer to pages 173-178 of the “Growth Models” chapter in textbook. Many growth phenomena can be modeled using a straight line. We will review the formula y=mx+b for straight lines, and match it to the explicit and recursive formulas given in the textbook. We will also consider the case where the growth is not exactly linear, but only approximately so. In such cases, we will have two possible strategies: the one used in example 2 on page 176 of the book, or the technique of linear regression, using the following online tool.
3. Polynomial Growth: Sometimes, a straight line is not accurate enough to capture a trend. In that case, we can use more powers of x in the formula used to model the growth. We will be particularly interested in quadratic and cubic growth, using the online tool once more. We will examine a problem from climate change, and one from the spread of AIDS. Included in readings: an article on climate change.
4. Exponential Growth: If a quantity increases by the same factor in a succession of equal time intervals, we get exponential growth. The reference for this will be pages 178-188 of the “Growth Models” chapter. A fun exercise will be to see how a tweet can go viral. We will also study the properties of logarithms as part of this topic, and discuss applications like the Richter Scale for earthquakes. Moreover, we will define the Fibonacci sequence and explore whether it grows exponentially.
5. Tax Rates: We will see how tax brackets correspond to “piece-wise” linear growth. As a class assignment, we will devise a taxation scheme that will help Congress balance the budget (see page 30-34 of “Problem Solving” chapter of textbook). We will briefly discuss simple and compound interest: refer to pages 197-203 of “Finance” chapter of textbook.
6. Logistic Growth: Populations in nature cannot sustain exponential growth indefinitely, so end up showing “logistic” growth. This can only be described by a recursive formula, or calculated using online programs. References: Pages 188-191 of the “Growth Models” chapter and notes on PowerPoint. Our computer simulations will lead us to encounter examples of chaos.

B. PROBABILITY AND STATISTICS: Many phenomena do not follow the exact formulas from part A, but rather, just follow them in an approximate, probabilistic way. In this section, we will define probability, and use it to build up different aspects of statistics. This gives a different way of looking at the world, which is increasingly used in Big Data and Machine Learning techniques that directly impact us. Once again, it is relevant for understanding the pandemic as well.

1. Probability: What should you believe if your test for a serious disease comes out positive? Definition and calculation of probabilities. Rules for calculation. The uncanny Monty Hill Problem from the TV show “Let’s Make a Deal.” References: Pages 251-262 of course reserve and Pages 279-292 of “Probability” chapter in textbook.
2. Expectation or Mean: Definition for a probability model. Applications to games of chance: Should you play the lottery? Law of large numbers. Reference: Pages 262-265 of course reserve and pages 305-308 of “Probability” chapter in textbook.
3. Normal Distribution: sampling, shape of normal curve, standard deviation. A fun exercise with Galton Boards. The 68-95-99.7 rule. Central Limit Theorem. Confidence Intervals. Applications to casino games like roulette. Reference: Pages 265-281 of course reserve.
4. Correlation: We’ll do this very briefly, in particular understanding the definition between correlation and causation. Selections from this website.
5. Proxies, Machine Learning and Big Data: Math is taking over your world, whether you like it or not. The results are not always pretty. Reading from “Weapons of Math Destruction” in course reserve.

C. MATH IN EVERYDAY LIFE: In this final section, we move away from numerical calculation and consider other forms of mathematics. In particular, the examples we consider shed light on the way math underlies so much of what we do and what surrounds us.

1. Elections: Gerrymandering: One of the most consequential issues facing the US today is that of gerrymandering, where political parties in power are drawing gerrymandered maps for congressional districts that favor their own party. We will see how mathematics (both geometry and statistics) can be used both to carry out such gerrymandering and stop it.
2. Elections: Fair Voting Methods: What constitutes a fair vote? This will come in handy if you’re ever hiring someone for your job. Reference: Chapter on “Voting Theory” from textbook. Articles from newspapers.
3. Logic (depending on time): The Wason Selection Task – I’ll predict before hand how many in the class will get it right. Related questions in mathematical logic.
4. Fractals (depending on time): Why are patterns in the universe the way they are? Input/output rules. How do mollusks generate fractals on their shells? Reference: Pages 367-372 of “Fractals” chapter from textbook.

#### Goals

Below are some specific goals that this course is geared towards helping you achieve.

1. Enhance computational and problem-solving mathematical skills.
2. Gain knowledge of mathematical techniques that may be of use in your future.
3. Acquire a preliminary understanding of statistics and its practical uses.
4. Get an introduction to how mathematical processes shape both society and nature.

#### Assignments and Tests

Most of these will be Blackboard based. You will be able to complete C assignments in class. Also, classes will be recorded, so if you miss a class, you can complete C assignments by the end of the day.

1. Homework assignments will be due by 5:30 p.m. on class days. Reading (R) assignments will generally test whether you have completed assigned readings before coming to class. Application (A) assignments will measure how well you can apply materials read or discussed.
2. Classwork (C) assignments will be introduced almost every class. These will generally be due by the end of the day.
3. The mid-term and final will both be open book, with access to any materials you want. See “Academic Conduct” below. The mid-term will be on Section A, after Spring Break. There will be two finals. The first “practice final” will be held in class on Mon, May 16. If you like the overall grade you get based on this, you don’t have to take the second “true” final, held  on Mon May 23, from 6-8 in our classroom. If you DO take Final 2, then the best score out of the two finals will be used for your overall grade.

#### Grading

Your overall grade will be based on the following formula: Homework: 30%, Classwork: 30%, Mid-term Test: 18%, Final: 22%. (Up to 5 points may be deducted from the “Classwork” category if you do not regularly attend and participate in lectures.)

The cut-off overall scores will be 90% for an A, 80% for a B, 65% for a C and 50% for a D.

#### Class Etiquette

Feel free to use chat! The more comments, the better. Be lively!

#### Important Dates

Feb 11 is the last date to drop a class without a W on your transcript. Apr 11 is the last date to drop this class with a grade of W. Please talk to me first if you are thinking of dropping the course!

#### Academic Conduct

Mid-term and Final are open book. You are welcome to use any resources (internet websites, notes, answers to previous tests, etc.). Please keep a record of your calculations, which can be submitted if needed.

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC’s scholarly community in which everyone’s academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, or the UMBC Policies section of the UMBC Directory.

#### Accommodations for Disability

If you require accommodations for this class based on disability, please make an appointment to meet with me to discuss your SSS-approved accommodations. Please see http://my.umbc.edu/groups/sss/documents/838 for more information.

#### Spring 2022 Safety Protocols and Compliance Statement

Please click here.