MAT 101M: Mathematics for the 21st Century

Fall 2018

Basic Information

• Instructor: Jed Yang, CC221, 651-638-6405,
• Office hours: Tuesday and Friday 13:30–14:30; or by appointment (instructions)
• Lectures: Mod B (MWF 09:00–09:50) in AC329
• Course website: https://www.mathcs.bethel.edu/yang/mat101.18f/

Course Information

• Official course description: Mathematical ideas that a liberally educated person should be familiar with in order to function well in a technological society.
• Prerequisites: Two years of high school algebra, including logarithms and exponential functions.
• Textbook: Jeffrey Bennett and William Briggs, Using and Understanding Mathematics: A Quantitative Reasoning Approach, 6th edition, 2015, ISBN: 9780321914620.
• Materials: Scientific calculator. Electronic devices such as computers and mobile phones are not to be used during exams.

Topics and Objectives

This course fulfills the General Education requirement for an M (mathematics) course. "Mathematical knowledge and skills are essential to decision making in daily life and many professional situations. It is necessary to ensure that all graduates have at least a minimum level of competence in them." (Preparing Today's Christians for Tomorrow's World, Bethel's General Education Curriculum Document, 17).

The emphasis of this course will be to apply mathematical strategies from arithmetic, algebra, statistics, and/or geometry to investigate, analyze, and solve problems from a variety of real-world contexts. It is hoped that students will come to a greater appreciation for the role of mathematics in our world. Galileo Galilei (1564–1642) said, "Mathematics is the language with which God wrote the Universe." Given a commitment to working hard (Colossians 3:23–24, see below), students will interpret, make connections among, and draw inferences from mathematical models, including verbal/written descriptions, formulas, graphs, diagrams, and data tables. Students will also represent mathematical situations verbally, numerically, symbolically, and graphically.

These objectives will be accomplished through solving problems together in class, through homework and projects, done individually and in groups, and through the use of appropriate supporting technology. Topics will include problem solving with units, numbers in the real world, managing money, spreadsheets, linear and exponential growth, statistical reasoning, basic statistics, and probability.

Grading

Your grade will be determined by a weighted arithmetic mean of various components with weights listed in the table on the right. The total score will be converted to a letter grade whose lower bounds are: 93% A, 90% A-, 87% B+, 83% B, 80% B-, 76% C+, 65% C, 60% C-, 57% D+, 50% D, 0% F.

Note that there is no preset curve of how many of each letter grade will be given. If you all do A-level work, you will each get an A. As such, you are encouraged to help each other in the pursuit of perfection.

In many courses I intentionally make one exam harder than others, which gives me information (in a mathematical sense) in separating an A performance from an A- performance. Typically, I will let you know and adjust that exam scores upward. What this means is that you should NOT care about how hard an exam is. If you do A-level work, you will get an A, regardless of the raw numerical score prior to adjustment.

Besides possibly adjusting scores upward for difficult exams, I also reserve the right to lower the grade cutoffs. Both of these help you. I will not hurt you by adjusting your exam scores downward or increasing the grade cutoffs.

Requirements

Whatever you do, work at it with all your heart, as working for the Lord, not for human masters, since you know that you will receive an inheritance from the Lord as a reward. It is the Lord Christ you are serving.

- Colossians 3:23–24 NIV

I will be trying to make these verses true for me as I work with you throughout this course, and I hope that you will, too.

Attendance and participation. I expect you to attend class. You may not notice me taking attendance during class meetings, but I will notice if you are not in class. Occasional absences will not impact your grade because what I look for is not mere attendance, but engagement and participation.

Indeed, coming to class is not just about showing up; it is also about being fully engaged in the learning experience. If you have a question, others in the class may also be wondering the same thing. So, please speak up and ask questions anytime you need to. Not only will you be helping yourself, but also you will be helping your peers. Attending office hours is another great opportunity to ask questions.

Be mindful of others. Refrain from using mobile phones or laptops for activities unrelated to the learning process. If you prefer to use laptops to take notes, please kindly sit in the back, as the screen may distract others. There is research that suggests taking notes by hand is better for long-term retention (P. A. Mueller and D. M. Oppenheimer, The pen is mightier than the keyboard, Psychological Science 25 (2014), 1159–1168).

Silence and put away mobile phones and do not use laptops for anything other than class-related activities.

It is my sincere hope that every one of you get all the points for attendance and participation.

Reading. Read the book! You should prepare for class by looking over the sections we will cover. It will be helpful if you read the text with a pencil in hand to try the examples yourself and work on assignments every day to keep you from falling behind. Be forewarned that a college math class is different than a high school math class. Because of limited class time you will need to learn some material on your own. Classroom instruction will be designed to complement and reinforce, not replace, the discussion presented in the textbook. It is therefore expected that you carefully read every section assigned. Mathematics cannot be learned by being a spectator: you must be actively involved. Focus on the process of solving problems as well as the result, understanding instead of memorization, and try to trust your own intuition. It is not true that some people cannot learn mathematics; it is true that it requires hard work to learn the subject!

Homework. Homework will be assigned most days. The goal of the homework is to give you an opportunity to continuously engage directly with the material. Some of the homework questions are meant to be challenging and to stretch you; simply put, I believe that the homework is where you will do the vast majority of your learning in this class. Grapple with the questions; talk to classmates about solution strategies if you are feeling stuck; do the homework.

Please staple your homework before coming to class and write your name, PO number, and homework number in the top right corner.

Homework is due at the beginning of the next class after it was assigned, unless otherwise stated. In general, late work is not accepted. If there are special circumstances, talk to the instructor. To alleviate your anxiety from accidentally forgetting to bring your homework to class, illness, emergencies, or other situations beyond your control, 25 points from the required total homework points shall be subtracted.

Because communicating results to others is an important skill, showing your work is as important as getting an answer. In many instances, credit will only be given if your work accompanies your answer. Some of the points will be given for completing the assignment; most will be awarded for showing work and correctness. You are encouraged to collaborate, but what you turn in must be your own work. See "Learning integrity" and the collaboration policy below.

Projects. There will be one or more projects designed to give you opportunities to apply the concepts from the homework and class sessions to practical questions. You will receive information in class for each project. Late projects will receive a 10% deduction in points for the first 24 hours after it was collected in class, 20% for the second 24 hours, and so on.

Exams. There are three in-class midterm exams (see calendar below for a tentative schedule), weighted equally. Subsequent exams will mainly focus on the material covered since the previous exam, but can include previous material too. There will be a final exam during the official final exam period covering the entire course.

You must have your own scientific calculator to use for exams. No sharing, no mobile phones, no laptops.

There are no make-up exams except in circumstances recognized by the instructor as beyond the control of the student. To receive this consideration, the instructor must be notified of the problem before the exam unless this is impossible, in which case as soon as possible.

Time outside of class. I expect a typical student to spend about two to three hours outside of class for each hour in class. Some students need to spend a bit more than that (which is okay). If you are spending more than 12 hours per week on this course outside of class time, please come talk to me so we can find ways to help you learn the material without spending so much time.

Illness. You should make every effort to attend class when you are healthy. If you become ill, for your well-being and the well-being of the rest of the class, you should not come to class. (Nor should you show up in my office with your germs!) Yes, this sounds like common sense, but it is tempting to try and power through as normal so as not to fall behind. If you become ill, or know that you will need to miss class for some reason, please contact me as soon as you are able, and we will work together to plan how you will keep up and/or make up any missed work.

Policies

Learning integrity.

Search me, O God, and know my heart;
Try me, and know my anxieties;
And see if there is any wicked way in me,
And lead me in the way everlasting.

- Psalm 139:23–24 NKJV

Collaborative work is an integral part of many successful ventures. As such, I expect that you should collaborate with your classmates a lot during your time in this course. However, it is important to understand that there is a big difference between thinking about and solving a problem as part of a group (which is good, both educationally and morally) and copying an answer or letting someone else copy your answer (which is bad, educationally and morally, and has punitive consequences).

In short, I trust you to maintain the utmost level of academic integrity in this course. Please do not break this trust; if you do, there will be repercussions. The formal policy below lays this out explicitly, and supplements Bethel's academic honesty policy.

Collaboration policy.

• You may collaborate on the homework assignments to the extent of formulating ideas as a group, but you may not collaborate in the actual writing of solutions (unless explicitly allowed in the instructions).
• In particular, you may not work from notes taken during collaborative sessions.
• You may not consult any materials from any previous offerings of this course or from any other similar course offered elsewhere unless explicitly permitted.
• You are required to completely understand any solution that you submit and, in case of any doubt, you must be prepared to orally explain your solution to me. If you have submitted a solution that you cannot verbally explain to me, then you have violated this policy.

Accommodation policy. Disability-related accommodations are determined by the Office of Disability Resources and Services (DRS). Students are responsible to contact the Office of Disability Resources and Services. Once DRS determines that accommodations are to be made, they will notify the student and the instructor via e-mail. Students choosing to use the disability-related accommodations must contact the instructor no later than five business days before accommodations are needed. The instructor will provide accommodations, but the student is required to initiate the process for the accommodations.

Concerns and appeals. If you have any concerns regarding the course, your grades, or the instructor, see the instructor first. If needed, see Bethel's academic appeals policy.

Getting Help

If you need help there are multitude of resources you can use:

• Yourself. If you're stuck on a problem or struggling with a concept from class, take a break and think about something else (e.g., your Hebrew assignment, the economics of Star Trek) for a few hours and then try a fresh start.
• Your classmates. You are each other's best resource: talking through the course material with someone else who is also trying to master it is a great way for you both to learn. (And don't discount the learning that you will do while trying to explain to a classmate an idea covered during class that you think you understand; I can't count the number of times that I've discovered that I didn't really understand something until I tried to teach it to someone.) The homework assignments are meant to challenge you, and figuring some of them out together is a great approach.
• Math Lab. The Math Department offers support for students enrolled in math classes by providing a Math Lab four days per week in HC 113 and 114. If you are having any difficulty with your homework in this class, please seek help from the tutors in Math Lab. The Math Lab is not only a great place to get help from tutors, but also is the perfect place to meet other students from class, do homework, and check your work. Plan Math Lab hours into your weekly schedule and develop this habit early on in the course.

  If you attend Math Lab at least once within the first five days it is open (8/30, 9/4-6,9), you will receive 5 extra credit homework points. Be sure to sign-in and you must stay for at least 15 minutes. This is a one-time extra credit offer, not for each time you're there. The point is to get you there early in the semester so you discover it is helpful.

• The instructor. Come to my office hours or email to make an appointment. To make an appointment, please email me several times you are available and try to give me at least 24 hours of lead time. Each afternoon, I will look at your availabilities and try to schedule as many people as I can fit for the next day. I will consistently reserve Thursdays for research, and I do not schedule office hours or make appointments for that day. I have this scheduled "research day" so that I can work on my research projects in an uninterrupted block of time. Without reserving a large block, I won't have time for any research. Tuesdays tend to be good days for appointments.

Calendar

Daily/weekly schedule to be updated throughout the term; topics and exam dates are tentative and subject to change.

Before class, please read the textbook section(s) to be covered. After class, start doing the homework assigned that day as soon as possible. Unless otherwise stated, homework will be due at the beginning of next class.

Date	Agenda	Homework
Week 1: Chapter 2 units and problem solving
1. 08/27 M	Introduction	hw01: Getting started
2. 08/29 W	2A working with units	hw02: Questions and notes
3. 08/31 F	2B problem solving with units	hw03: 2B Q # 1, 2, 4, 9, 10; E # 5, 6, 15, 16, 19, 23, 24, 26, 27, 34, 39, 43, 45, 46, 51, 53.
Week 2: Chapter 3 numbers in the real world
4. 09/05 W	3A percentages	hw04: 3A Q # 1, 2, 4, 10; E # 4, 10, 11, 26, 29, 46, 49, 51, 55, 58, 62, 64, 65.
5. 09/07 F	3B numbers in perspective	hw05: 3A E # 16, 69, 73, 75–77, 79, 95, 99.
Week 3: Chapter 4 managing money
6. 09/10 M	3C uncertainty in numbers	hw06: 3B E # 15, 18, 20, 31, 38, 63, 82 (for 82, only need one, give source). And on a separate sheet of paper do: 3C Q # 2, 3, 8–10; E # 17, 19, 20, 22, 23, 29–32, 60–63. You will turn in the 3B and 3C work in two separate piles, so staple accordingly. Label clearly which one is 3B and which one is 3C.
7. 09/12 W	3D index numbers	hw07: 3D Q # 4, 9, 10; E # 10, 12, 17, 18, 21, 24, 31, 34, 38.
8. 09/14 F	4A principles	hw08: 4A Q # 4–6; E # 5, 8, 21, 24, 28, 31, 35, 42, 49, 53. Due Wednesday.
Week 4
9. 09/17 M	Exam 1 (topics and tips)
10. 09/19 W	4B compounding	hw10: 4B Q # 1, 2, 10; E # 3, 15–23, 34, 35, 41, 43, 44, 46, 51, 52, 57, 60, 63, 66, 83. Extra credit: 56. If you do it, put it at the end.
11. 09/21 F	4B continuous compounding	hw11: 4B Q # 6; E # 10, 71, 72, 75, 76, 86, 91, 100.
Week 5
12. 09/24 M	4C savings plans, investment	hw12: 4C Q # 5, 6; E # 5, 10–12, 15, 20, 25, 35–37, 57, 67, 69*. * 69d: no need for a paragraph; a sentence suffices.
13. 09/26 W	4D loans	hw13: 4D Q # 2, 5; E # 10, 12, 13, 15–17, 38. Read and fill in the blanks for A Loan Tale; answers in the slides posted on Moodle. Bring laptop next class!
14. 09/28 F	4D amortization	hw14: 4D Q # 4, 6, 7; E # 26*, 29*, 34*. * 26: calculate and write this by hand without a spreadsheet. * 29: do more than the book asks: also create an amortization schedule as we have done in class. * 29, 34: do with spreadsheets; print and attach.
Week 6: Chapters 8–9 exponentiation
15. 10/01 M	4D home ownership	hw15: Handout. Read over Project 1 and bring questions next class.
16. 10/03 W	8A exponential growth	hw16: 8A Q # 1–3, 7, 8; E # 9–11, 13, 17, 19, 20, 25–27.
17. 10/05 F	8B doubling time	hw17: 8B Q* # 1, 2, 5, 7, 8; E # 13, 14, 19, 26, 29, 34, 37, 42, 43. * No need to explain Q questions this time.
Week 7
18. 10/08 M	Chapter 4 Quiz 8C logistic growth	hw18: 8B E # 20, 51, 54; 8C Q # 1, 3–5; E # 8–10, 16, 17a, 20a, 22, 23. Extra credit: 8C E # 30.
19. 10/10 W	9C exponential modeling	hw19: 9C Q # 2–7, 10; E # 7, 10–12, 15, 19, 22, 35–37, 41, 47. Extra credit: 9C E # 40. Project 1 due on Monday!
Week 8: Chapters 5–6 statistics
20. 10/15 M	Review Project 1 due	hw20: None: study for exam!
21. 10/17 W	Exam 2 (topics and tips)
22. 10/19 F	5A statistics basics	hw22: 5A E # 27, 29–34, 38, 39, 48, 49, 55, 56; and one of 62–64.
Week 9
23. 10/22 M	5C tables and graphs 5D graphs that deceive	hw23: 5C E # 25, 40, 43. You are encouraged to use the Google Sheets template shared with you. Print and hand in as usual. (You may use other software or draw charts by hand.)
24. 10/24 W	6A averages	hw24: 5D Q* # 1–8, 10; E # 14, 27, 29, 35. * No need to explain Q questions this time.
25. 10/26 F	6B standard deviation	hw25: 6A Q # 4; E # 7, 8, 14, 15, 19, 21, 25, 27, 37–39, 43. Extra credit: 6A E # 44.
Week 10
26. 10/29 M	6C normal distribution	hw26: 6B Q # 3, 6; E # 11, 12, 15*, 18*, 21, 22. * 15be: no need for boxplot in part b; no need to do part e. * 18be: draw boxplot in part b; do part e. * 15c, 18c: Calculate standard deviation of Mahler by hand and show all the steps, i.e., with a table like we did in class; for Beethoven and for #15, you may use a calculator or spreadsheet and just write down the final answer without showing any work.
27. 11/02 F	6D inference	hw27: 6C Q # 2, 5–10; E # 19abdgh, 21–25, 31, 33, 34, 37ab, 38, 41.
Week 11: Chapter 7 probability
28. 11/05 M	Review	hw28: A spreadsheet of male heights has been shared with you via Google Drive. See instructions therein.
29. 11/07 W	7A probability basics	hw29: None: study for exam! After the exam, start doing the next homework, which is long.
30. 11/09 F	Exam 3 (topics and tips)
Week 12
31. 11/12 M	7B conditional probability	hw31: 7A Q # 2–5, 7; E # 8, 11, 15–17, 20, 22–25, 28, 29, 35–37, 39, 43, 51, 52, 65, 67, 74, 75.
32. 11/14 W	7B combining probabilities	hw32: 7B Q # 2, 4; E # 8, 13–17, 20, 33, 34, 58, 60.
33. 11/16 F	7B repeated trials	hw33: 3E E # 18. 7B Q # 8–10; E # 7, 21–24, 39, 42, 43, 48, 51.
Week 13: giving thanks
34. 11/19 M	7C law of large numbers	hw34: 7B E # 28, 29, 32, 37, 55, 62, 63. 7C Q # 4, 5; E # 16, 19, 37.
Week 14: Chapter 12 voting
35. 11/26 M	7E permutations	hw35: 7C E # 17, 18, 23, 31. 7E Q # 1, 2; E # 11, 13–15, 19, 23–27, 33.
36. 11/28 W	7E combinations	hw36: 7E E # 28, 29, 30, 31, 34–36, 38, 39, 46–48, 50, 55.
37. 11/30 F	12A voting methods	hw37: 12A E # 28, 30–34, 37, 44, 45.
Week 15
38. 12/03 M	12B voting fairness Project 2 due	hw38: 12B E # 10, 13, 16, 19, 24, 27, 32, 35, 42, 45.
39. 12/05 W	Chapter 7 Quiz	hw39: None: study for exam!
40. 12/07 F	12D gerrymandering	hw40: None: study for exam!
Final Exam: 12/14 Friday 08:15–10:15 (topics and tips)