An introduction to quantitative reasoning, with the aim of developing the capacity to comprehend and analyze the quantitative information that is prevalent in modern society. Topics include mathematical modeling, basic probability and statistics, and practical applications.

- Math 104: Algebra II (not developmental; gives college credit but is not College Algebra)
- Math 105: College Algebra
- Math 107: Trigonometry

- Basic percents: such as
- 1.2 is what percent of 4.9?
- If the budget is now 10.1 when it was 10.3, what is the percent change?
- If something cost 5.7 and it increased 6.1 percent, what does it cost now?

- Scientific notation: ability to convert 4e8 to 400,000,000 for example.
- Direct Proportionas: ability to set up and solve.

Math 110 is one of the math courses that fulfills the General Education requirement for mathematical reasoning, in many cases. It also fulfills prerequisites for courses in Chem, CompSci, Econ, Business, and Psych, among others.

3 credit hours.

Class meetings will be mostly interactive lectures, with some time to work on problems in class, and some time to go over problems from the homework. Some class sessions will meet in a computer lab or use a cartful of laptops. Exams will also be held during class meetings.

I expect that you will work on Math 110 for 6 to 10 hours per week outside of class.Office: Pray-Harrold building, room 515z

andrew.ross@emich.edu

http://people.emich.edu/aross15/

(734) 487-1064, but I strongly prefer e-mail instead of phone contact.

- "Quantitative Reasoning in Mathematics" Course Pack by Ahlbrandt, Calin, Curran, Gardiner, and Ross. There's no ISBN. I strongly recommend you not buy a copy more than 1 year old
- Scientific Calculator. Bring it to class each day. A good example is the TI-30X-IIS calculator ($15-$20). It does not have to be a graphing calculator, but the TI-83plus graphing calculator is recommended. Cell-phone calculators are not allowed on quizzes or tests.
- Microsoft Excel, or other spreadsheet software such as MS Works or Gnumeric or OpenOffice.org Calc or Google Docs.

- Graphing Calculator Manual for TI-83plus and TI-86 (ISBN: 0534-379001)
- In past years, we have used other textbooks for this course;
some people may like to read them in addition to our current
textbook. They are:
- "Using and Understanding Mathematics: A Quantitative Reasoning Approach" by Bennett and Briggs (any edition),
- "For All Practical Purposes: Mathematical literacy in today's world" (any edition), and
- "Quantitative Reasoning: Tools for Today's Informed Citizen" by Sevilla and Somers

- Carry out the steps of a mathematical modeling process.
- Apply a variety of mathematical models to problem situations.
- Analyze data using descriptive statistics.
- Calculate and interpret discrete probabilities.
- Use the normal distribution.
- Apply statistical criteria such as significance tests, correlation and confidence intervals.
- Explain the meaning of statistical criteria such as significance tests, correlation and confidence intervals.
- Present a written or oral report outlining a problem situation, a proposed mathematical model, and a solution, together with a discussion of both the assumptions upon which the model is based and the limitations of the model.
- Analyze data using a spreadsheet program.
- Use a spreadsheet program to produce tables and graphs, and include them in a written report.

- Identify an appropriate model.
- Identify and discuss assumptions.
- Collect or generate appropriate data.
- Analyze a situation using arithmetic, geometric, algebraic, and probabilistic or statistical methods.
- Estimate answers.
- Propose and evaluate solutions.
- Predict outcomes in other situations based on what they have learned from their analysis.
- Understand and communicate quantitative relationships using symbols, equations, graphs, and tables.
- Share their findings in oral and written reports using appropriate mathematical language.
- Write summaries to explain how they reached their conclusions.
- Draw inferences from a model.
- Discuss the limitations of the model.

- Percents pre-test
- Ch 1.1: Fish in the Lake: accuracy and precision
- Ch 8.1: Intro to Spreadsheets: text/number/formula, cell references, formatting
- Ch 1.2: Big Numbers (Scientific Notation), analytic estimation
- Ch 1.3: Compared to What? Putting numbers in context
- Ch 8.2: Intro to Spreadsheets: Simple and Compound interest
- Ch 2.1: Direct Proportions
- Ch 2.2: Inverse Proportions
- Ch 2.3: Advanced Percents:
- Spreadsheet formulas and formatting
- percentage points
- comparisons other than increase/decrease, like "Your proposal costs 90% more than mine"

- Ch 2.5: Inflation and Consumer Price Index (CPI)
- using CPI to convert from one year to another
- computing inflation as a percent from CPI
- "nominal" vs "real" percent changes
- "in constant dollars"

- Ch 3.1-3.3: Linear models review
- Ch 3.4: Piecewise Linear models:
- Economies of Scale/Bulk Discounts
- Diseconomies of Scale/Increasing Marginal Costs
- Progressive/Flat/Regressive taxes
- use of =max() and =min() in spreadsheets

- Ch 3.5: linear regression on spreadsheets
- Ch 4: Exponential models, mainly compound interest (I actually skip this, preferring to do them year-by-year on a spreadsheet)
- Ch 5.1: Sampling, Random Sampling, Bias
- Ch 5.2: Probability
- Axioms (called "basic rules")
- Empirical probability
- Expected Frequency
- specifically skipped: combinatorics, binomials, etc.

- Ch 5.3: Expected Value and insurance
- Ch 6.1: histograms
- Ch 6.2: Mean and Median
- Social Security Game
- a week of preparation: worksheets from the gamebook, game instructions, etc.
- a week of role playing

- Ch 3.5: correlation vs. causation
- Ch 5.4: Gambler's Fallacy, classical vs. frequentist vs. Bayesian
- Ch 7: confidence intervals, statistical significance vs. practical significance

- 50%: Homework, In-Class Work, Projects, and possible Quizzes
- 15%: each of 2 Midterm Exams
- 20%: Final Exam

I take attendance every day. Research shows that taking attendance improves student success, so that is why I do it. There will be material presented in class that is not in the textbook, yet will be required on the exams. Similarly, there are things in the textbook that are might not be covered in class, but are still required on the homework and exams. If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you.

My lectures and discussions mostly use the chalkboard. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.

Sometimes we may have work that is assigned but not collected. Even if homework or worksheets are not collected, you are responsible for learning it--it could be on the tests!

Our project this semester will be a role-playing game where we pretend that it is 1935 and we are members of the US House of Representatives. You will stand up and make short speeches to persuade your fellow Representatives to vote for what you want included (or not included) in the new Social Security law, using cost estimates that you derive as your main line of reasoning. This will occupy a week of class about 2 weeks before the last day of class.

The final will be comprehensive, with a special emphasis on any material not covered by the midterm exam(s).

You might be assigned seats while exams are in progress. No extra time will be given for late arrivals to exams. During the exam, all electronic equipment other than your calculator should be put away. Remember, calculators embedded in cell phones are not allowed.

Do not purchase any airline tickets to depart before the final exam. Be sure to allow enough time to get to the airport, etc. You will not be allowed to "take the exam early because you have already purchased a non-refundable airline ticket". See above for the final exam schedules.

No scores will be dropped, unless a valid medical excuse with evidence is given (subject to the school's H1N1 Flu policy). In the unfortunate event of a medical need, the instructor will decide between a make-up being given or the grade being dropped, or any appropriate other options. Even if a grade is dropped, you are strongly encouraged to still complete the relevant assignments or exams and consult with me during office hours to ensure you know the material.

- Study, prepare and take advantage of office hours if needed!
- Come to class, take notes & use the opportunity to make the sheet for exams. Very helpful were the sheets we could use on exams.
- Write all that you can on the note sheet you can use for the test because it's better to have more than you need instead of missing something :)
- Be prepared to understand the math and its various applications.
- You will be spending a lot of time on the computer, but the areas that you cover will really benefit you.
- Read the book (at least some of it). The examples from the book are very helpful. Sometimes things are better explained in the book if you don't completely understand how to do something first.
- Listen to what is talked about in class to help prepare for the exams.
- Have a calculator & do the homework. Watch your calculations.
- Make sure you always ask questions and go to office. It is what helped me get through this class. Professor Ross always helped when we asked.
- Come to class, ask questions, see Dr. Ross in office hours he will help explain things.
- Don't round up on the homework until you get to your final answer.