Harris School of Public Policy
Math Camp 2009

Basic Purpose

Each day, I plan to lecture for a while, take a break, and then present problems to work on in small groups, after which we will re-unite to go over some of this group work.

Schedule

The class meets every weekday from August 31 through September 18 from 9-12 A.M. with the following exceptions:
Monday, September 7, is Labor Day, and there is no class.
Tuesday, September 8, class will be held from 9-11 so that you can all participate in the Scavenger Hunt.

The first sitting of the Algebra Exam took place on Friday, September 4.
The maximum score was 157, the passing score was 96, and the mean and median were both 107. Here are the scores, sorted by student ID number.
Here is a copy of the exam together with a solution set and the associated graphs.

The second sitting of the Algebra Exam took place on Monday, September 21. Here is a copy of the exam.
The maximum score was 133, the passing score was 81, the mean was 94, and the median was 97. Here are the scores, sorted by student ID number.
(If your ID is not listed, please contact Ellen Cohen.)

The Calculus Exam also took place on Monday, September 21. Here is a copy of the exam.
The maximum score was 167, the passing score was 79, the mean was 91, and the median was 100. Here are the scores, sorted by student ID number.
(If your ID is not listed, please contact Ellen Cohen.)

Contact Information

My office is Ryerson 354, and you can e-mail me at: boller@math.uchicago.edu

The TA's for Math Camp are:
Arianna Zanolini, e-mail: azanolini@uchicago.edu
Congyi Zhou, e-mail: czhou@uchicago.edu
Ana Sophia Leon, e-mail: asleon@uchicago.edu
Amer Hasan, e-mail: ahasan@uchicago.edu

Text

I will not be working directly from a textbook, and my recommendation is merely that you obtain a decent copy of almost any Calculus book and work practice problems from relevant sections. However, the one that will be used in the autumn class for those who do not pass the Placement Exam(s) is "Applied Calculus," 9th Ed., by Laurence D. Hoffman and Gerald L. Bradley, McGraw-Hill 2007, ISBN 0-07-305192-6. This book has been used in past years, and it has examples that are probably more relevant to students of public policy than most others. In the schematic of this text, we will cover roughly the first four chapters and the first two appendices in approximately the following order: App. A1, App. A2, Ch. 1, Ch. 2, App. A3, Ch. 3, Ch. 4.

Placement Exams

There are two exams that you must pass. (If you do not, then you must take an additional mathematics course in the Autumn Quarter.) The first is the Algebra Placement Exam, and the second is the Calculus Placement Exam. My understanding is that if you did not pass *both* exams, then you must take the autumn course, but please see Ellen Cohen about this to be sure.

The first sitting of the Algebra Exam will take place on Friday, September 4, from 1:30 until 3 P.M.
The second sitting of the Algebra Exam will take place on Monday, September 21, from 9 until 10:30 A.M.
The only sitting of the Calculus Exam will take place on Monday, September 21, from 10:40 A.M. until 12:10 P.M.

Here are some exams from past years from which to prepare:

Here is a copy of the first edition of the 2008 algebra exam with solutions and the graphs for #2(d), 3(b), 7(b), and 8(d). The passing mark was 86 (out of 144).
Here is a copy of the second edition of the 2008 algebra exam. The passing mark was 73 (out of 131).
Here is a copy of the 2008 Calculus exam. The passing mark was 77 (out of 140).

Here is a copy of the first algebra exam 2007 with solutions and the graphs for #1(f), 2(d), 6(a+b), and 8(d).
Here is a copy of the second algebra exam 2007 with solutions and the graphs for #2(d), 4(b), 6(a), and 8(d).
Here is a copy of the first Calculus exam 2007 with solutions.
Here is a copy of the second Calculus exam 2007 with solutions and the graphs for #2(b) and 7.

A sample Placement Exam (with the Calculus Exam as well) from 2006.
A sample Algebra Placement Exam and a sample Calculus Placement Exam culled from other previous exams.

Algebra and Pre-Calculus

Notes: Axioms for the Real Numbers, Number Systems
Reading: Appendices A1 and A2 from the text
Problem: Use the Axioms to prove the algebraic formula for the factorization for the difference of two cubes:
x^3-y^3=(x-y)(x^2+xy+y^2)
Notes: Definitions and Theorems 1 (Algebra, Absolute Value, Intervals).
Problems: Problems 2.
Notes: Definitions and Theorems 2 (Lines).
Reading: Chapter 1, Sections 1.1-1.3 (Functions, Graphs, Linear Functions).
Problems: Problems 3.
Notes: Definitions and Theorems 3 (Exponentials and Logarithms).
Reading: Chapter 4, Sections 4.1-4.2 (Exponential and Logarithmic Functions).
Problems: Problems 4.

Calculus

Reading: Sections 1.5 (Limits) and 2.1 (The Derivative).
Problem: Use the technique from class to find the derivative of f(x)=x^3.
Notes: Definitions and Theorems 4 (Limits and Continuity).
Reading: Sections 1.5 (Limits), 1.6 (One-Sided Limits and Continuity) and 2.1 (The Derivative).
Problems: Problems 6.
Notes: Definitions and Theorems 5 (Differentiation).
Reading: Sections 2.2 (Techniques of Differentiation) and 2.3 (Product and Quotient Rules).
Problems: Problems 7.
Notes: Definitions and Theorems 6 (Differentiation of Logs and Exps, Chain Rule).
Reading: Sections 2.4 (The Chain Rule) and 4.3 (Differentiation of Logarithmic and Exponential Functions).
Problems: Problems 8.
Reading: Sections 2.6 (Implicit Differentiation and Related Rates).
Problems: Problems 9.
Notes: Definitions and Theorems 10 (Mean Value Theorem, Analysis of Functions).
Reading: Sections 3.1 (Increasing/Decreasing, Relative Max/Min) and 3.2 (Concavity and Points of Inflection).
Problems: Problems 10.
Reading: Sections 3.3 (Curve Sketching) and 3.4 (Optimization)
Notes: Definitions and Theorems 12 (Limits at Infinity, Infinite Limits, and Asymptotes).