Harris School of Public Policy
Math Camp 2011

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 29 through September 16 from 9-12 A.M. with the exception of Labor Day Monday, September 5, when there is no class. (Also, class on Tuesday, September 6, will only run until 11:15 so that you can participate in the Scavenger Hunt.)

The first sitting of the 2011 Algebra Exam took place on Tueday, September 6.
The maximum score was 153, the passing score was 90, the mean was 118, and the median was 124.5.
Here are the scores, sorted by student ID number.
Here is a copy of the exam together with a solution set.

The second sitting of the 2011 Algebra Exam took place on Monday, September 19.
The maximum score was 162, the mean was 98, and the median 97.
Here are the scores, sorted by student ID number.
Here is a copy of the exam.

The 2011 Calculus Exam took place on Monday, September 19.
The maximum score was 163, the mean was 130.5, and the median 116.5.
Here are the scores, sorted by student ID number.
Here is a copy of the exam.

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:

Maria Rosales Rueda, e-mail: mrosales@uchicago.edu
Gretchen Torres gretchenwt@gmail.com
Congyi Zhou czhou@uchicago.edu

Their office hours are in the afternoons at Harris but vary from week to week.

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 do not pass *both* exams, then you must take at least part of the autumn course.

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

Here is a copy of the first edition of the 2010 algebra exam with solutions and the associated graphs. The passing mark was 88 (out of 149).
Here is a copy of the second edition of the 2010 algebra exam. The passing mark was 92 (out of 158).
Here is a copy of the 2010 Calculus exam together with solutions and the associated graph. The passing mark was 71 (out of 154).

Here is a copy of the first edition of the 2009 algebra exam with solutions and the associated graphs.
Here is a copy of the second edition of the 2009 algebra exam. The passing mark was 81 (out of 157).
Here is a copy of the 2009 Calculus exam. The passing mark was 79 (out of 187).

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).