Harvard University Summer School

Math S-Y   Mathematical Models and Expressions

Course Information and Syllabus  

Summer 2006

 

Instructor:  Andy Engelward                           Phone: Home (781) 676-0676

                                                                                    Work (617) 998-8594

Office:  51 Brattle St. room 707                       E-mail: engelward@math.harvard.edu

 

Course Assistant: Margaret Barusch              E-mail: barusch@post.harvard.edu

 

Classes: Lectures – MWF from 11am to 1pm, Science Center room 309a

    First session will be on Wednesday, June 28th

    Review/problem sections – scheduled for Mon, Tue, Wed and Thurs. from 3 to 4pm in Science Center room 111

 

Required Text:  We will be using a specially prepared coursepack for this class.  This will contain a combination of texts by Eric Connally.  The coursepack will be available at the beginning of class and we will pass along information about it at our first meeting.  If you are interested in the style of the text please see Functions Modeling Change also by Eric Connally and available through the Harvard Coop – note that this is not our exact book, but ours will be similar in style.  Note that this course will also include topics from statistics that are not included in the Functions Modeling Change text.

 

Course Description and Goals:  This course has been designed to give students an opportunity to explore basic mathematical models as they arise in real-world situations with the goal of understanding the meaning behind mathematical expressions and functional relationships.  We will use computer spreadsheets (predominantly Excel) to study data sets as we work through basic functional relationships such as linear and exponential growth.  As we work with mathematical models we will also review basic algebra as well as topics from statistics. 

 

Much of the math that we will be working on during the first part of the course constitutes what is typically called “precalculus,” which includes such topics as linear and exponential growth, logarithmic scales, and polynomial functions.  Knowledge of these fundamental topics is not only critical for further study in math but it also forms the basis for much of the analysis that is done in science and economics today.  Confidence and experience in these areas is useful for making better sense of the modern world. 

 

Students interested in following up from this course with more mathematics should be prepared to go on to either an intensive precalculus class or classes in discrete mathematics or statistics.

 

Prerequisites and expectations:  Math S-Y is a 4-unit, undergraduate class. Prerequisites for the course include arithmetic and some algebra.  We expect that students will be prepared to work diligently and put in the effort to keep up with the list of precalculus and statistics topics that we plan to cover in the course.  To ensure appropriate background for this class, the Harvard Summer School Math placement test is required.

 

Homework: The best way to learn mathematics is by doing mathematics, and so doing homework for this class is an important part of the semester.  To make sure that you are keeping up with the topics we are covering during the summer, there will be an assignment due at the beginning of each class.  These will normally be graded and returned to you by the next class, with comments, so that you can learn from your work.  Homework that is late by one class period will normally be penalized by 25% and homework later than one class will not normally be accepted for credit.  The lowest homework score from the summer will be dropped from your average.

 

If you can't make it to class, you should still be sure to pass in your homework (either by email or through another student in the class).

 

Tests:  Along with homework, there will be many opportunities for you to show off what you have learned in class.  We will have short weekly quizzes on Fridays and there will be two in class tests during the summer as well.  The tentative schedule for these tests is:

 

            Test 1:  end of third week, July 14th 

Test 2:  end of sixth week, August 4th 

            Final Exam:  during final exam week, August 14th through 18th, day to be announced    

 

Note - there will be no make-up final exam, so please be sure to set aside that date.  Make-ups for the other tests will be made only in cases of family or medical emergencies.

 

Course grade:  This will be based on a combination of homework and tests as follows: 

homework:  20%,     tests:  20% each,    quizzes: 15%,    final exam:  25%. 

 

Handouts, Class website:  We will sometimes use supplementary materials that will be handed out in class.  If you have to miss a class, then it's your responsibility to find out what you might have missed - just be sure to catch up with me or with someone else in the class to check.  You can also check the course website for class information:  http://www.math.harvard.edu/~engelwar/MathSY.

 

Calculators:  At this point calculator technology has advanced to a considerable degree.  There is a wide variety of graphing calculators available for under $100.  As well as making it possible to do complicated arithmetic operations, these graphing calculators are extremely useful for checking function graphs, and for simple modeling. We won’t require you to have a specific graphing calculator for the course, so that if you already have one then you don’t need to purchase a new one just for this class.   In class we will probably use a Texas Instruments graphing calculator, so if you have a TI calculator already, then you will probably be able to follow along with any in-class calculator demonstrations fairly easily.  We will also make regular use of the computer software program Excel which is available on Harvard University computers.

 

Review/Problem Sections:  Make sure you take advantage of all of the resources which are available to you.  Our course assistant will be hosting regular problem sessions each afternoon, except Fridays, room to be announced.  There will be a fair amount of homework and computer assignments to keep up with during the summer and so it will likely be extremely useful for you to attend as many review/problem sessions as you can.

 

I look forward to seeing you in class this summer!

Math S-Y       Mathematical Models and Expressions

                                               

Summer 2006 Syllabus    

(note this is tentative - to be modified as needed during the summer)

 

Text by Eric Connally in a coursepack available at the beginning of summer school

 

 

Week

Date

Topics

1

June 28th, 30th

Introduction to course, working with Excel, first modeling assignment, expressions versus equations, directly proportional growth

 

2

July 3rd to 7th

Linear functions, solving linear equations, simultaneous linear equations, modeling with linear functions, interpolation vs. extrapolation

 

3

July 10th to 14th

Power functions, Quadratic functions, graphs, vertex form, modeling with power functions

 

Test one on Friday, July 14th

4

July 17th to 21st

Exponential functions, scientific notation, log scales, modeling with exponentials

 

5

July 24th to 28th

Introduction to probability, expected payoffs, decision trees and screening tests

 

6

July 31st to August 4th

Data representation – mean, median, and standard deviation, working with statistics, sigma notation

 

Test two on Friday, August 4th

7

August 7th to Aug. 11th

Final modeling assignments (and possibly including hypothesis testing and confidence intervals)

 

8

August 14th to Aug. 18th

Final exam to be held during regular summer school final exam period – day and time to be announced