Fall 2014 Course Syllabus - Mathematics 0824.006

Course: Mathematics 0824.006.
Course Title: Mathematical Patterns.
Time: MWF 10:40-11:50.
Place: GLFLTR 0L011.
Instructor: Gimenez, Jose.
Instructor Office: TBA.
Instructor Email: jose.gimenez@temple.edu
Instructor Phone: TBA.
Office Hours: MWF 1:00-2:00.
Prerequisites: Placement Exam or having taken Math 701 (Elementary Algebra) or an equivalent.
Textbook: None, course notes.
Course Goals: To improve the level of quantitative awareness of students using familiar situations that provide a sense of purpose for studying mathematics and develop an understanding of the uses and abuses of mathematics in everyday life.
Topics Covered: Basic Numeracy We'll start out discussing certain essential numbers: population of the US; the population of the world; distance from coast to coast; approximate number of deaths annually from various common diseases contrasted with the number of deaths in more dramatic contexts; the difference between a million, billion, and trillion; and so on. Incidentally, a million seconds takes approximately 11 1/2 days to tick by, a billion seconds is about 32 years, and a trillion seconds 32,000 years. We'll talk about estimating and comparing: How much human blood in the world? How many homeless people in NYC? How do various governmental expenditures compare? and so on. Related to this are so-called Fermi problems. Physicist Enrico Fermi was known for challenging his classes with problems that, at first glance, seemed impossible. One such was estimating the number of piano tuners in Chicago given only the population of the city. Dimensional analysis, basic conversions, scientific notation come next. For example, how fast does human hair grow in miles per hour? What is the cost of beef in drachma per kilogram as well as many disparate conversions. Many may seem irrelevant until one starts talking of the equivalents of the one trillion dollars spent in Iraq, for example (130 EPA's, 170 NSF's, 200 NCI's). We also discuss the mean, median, and mode as well puzzles and paradoxes involving these and related notions. Why do you have fewer friends than most of your friends? Why is the average class size often less than the class size seen by the average student? II. Probability and Statistics We examine some psychological aspects of statistics: the very important anchoring effect, availability error, and confirmation bias as well as examples from Tversky, Kahneman, and other cognitive psychologists. Relevance to the stock market. Basic notions from probability - sample spaces, examples (coins, dice, roulette wheels, heights, incomes). Probability rules (sum rule, product rule, at least one rule). Expected value. Conditional probability. Racial profiling. Bayes' theorem and false positives. Cancer test (98% accurate, 1 out of 200 with cancer, 10,000 tests administered.). Lie detector tests. Expected value, insurance, blood tests, Pascal's wager, etc. correlation versus causation. Coincidences and birthday problem. Probability of a particular event vs probability of some event of a general sort. Months - JFMAMJJASOND, Planets - MVEMJSUNP. Significant? No. And, of course, the birthday problem and the optimal strategy for picking the best spouse when meeting candidates sequentially. Various classic puzzles and stories: the Monty Hall problem, gambler's ruin, the gambler's fallacy and gambler's ruin, the Banach match box problem, the drunkard's random walks, the St. Petersburg paradox, the hot hand, others. Lotteries, a tax on innumeracy. Rare events. Finally, among the news stories covered will be many of the following: air safety, relative risks; health hazards of all sorts; statistics, the U.S. Census; redistricting, (conditional) probability in the courts; weasel phrases such as "studies show," "many," and "may be linked"; reliability of political polls; junk science. III. News, Elections, Scaling We'll also discuss various voting systems (plurality, Borda counts, runoffs, approval), strategic voting, American electoral system, chairman paradox; a mathematical definition of power (Banzhaf power index, supermajorities), a bit of geometry and scaling quantities upward and downward (area scales with the square, volume, weight with the cube of the scaling factor), as well as a number puzzles, paradoxes, Kruskal's card trick, prisoner's dilemma, psychological oddities, and a wide variety of news stories and contemporary issues.
Course Grading: 3 quizzes (20 % each), section work (15%), cumulative multiple choice final exam (25%).
Exam Dates: Approximate Exam dates are as follows: Test1: Sept.26,Test2:Oct.31,Test3: Dec.2. Final Exam: Monday 12/15 10:30-12:30.
Attendance Policy: Attendance is mandatory and will count as a portion of your grade. 4 absences during the semester will result in your grade being lowered by 1 notch, e.g., from B to B-, and for every increment of 4 classes or a portion thereof that you miss the grade will be additionally lowered. Attendance will be taken every day.

Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.

Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.

Students will be charged for a course unless dropped by the Drop/Add deadline date given below.

• Fall Begins: Monday August 25, 2014
• Classes Begin: Monday August 25, 2014
• Labor Day: Monday September 1, 2014
• Course Add/Drop Deadline: Monday September 8, 2014
• Course Withdraw Deadline: Friday October 24, 2014
• Fall Break: Monday-Friday November 24 - November 28, 2014
• Classes End: Monday December 8, 2014
• Study Days: Tuesday-Wednesday December 9 - December 10, 2014
• Exam Week: Thursday-Wednesday December 11 - December 17, 2014
• Diploma Date: Thursday December 18, 2014

During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.

The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.