Harris School of Public Policy
Math Camp 2007
Summer 2007
Instructor: John Boller, Senior Lecturer in Mathematics
Course Information
Math Camp is a three-week review of pre-Calculus and Calculus
material as preparation for the first-year coursework in
the Harris School of Public Policy.
The first week will cover algebra and pre-Calculus topics
from the rules of algebra, solving equations,
functions and graphs, through exponential and trigonometric functions.
The second and third weeks will cover the essentials of differential
Calculus.
The first edition of the Algebra Placement Exam took place
on Friday, August 31, and it has now been graded.
Here are the
scores,
sorted by student ID number. The columns represent: ID#, score on
questions 1-3 (out of 66), score on questions 4-6 (out of 48), score
on questions 7-9 (out of 42), total score (out of 156), and percent score.
The passing grade is a raw score of 94 (out of 156), which converts to
a percent score of 60%.
The second edition of the Algebra Placement Exam took place
on Monday, September 17, and it has now been graded.
Here are the
scores,
sorted by student ID number. The columns represent: ID#, score on
questions 1-3 (out of 61), score on questions 4-6 (out of 48), score
on questions 7-9 (out of 46), total score (out of 155), and percent score.
The passing grade is a raw score of 91 (out of 155), which converts to
a percent score of 59% (when rounded).
The first edition of the CalculusPlacement Exam took place
on Monday, September 17, and it has now been graded.
Here are the
scores,
sorted by student ID number. The columns represent: ID#, score on
questions 1,4,5 (out of 48), score on questions 2,3,6 (out of 40), score
on questions 7,8 (out of 45), total score (out of 133), and percent score.
The passing grade is a raw score of 76 (out of 133), which converts to
a percent score of 57%.
Here is a copy of the
first algebra exam
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
with
solutions,
and the
graphs for #2(d), 4(b), 6(a), and 8(d).
Here is a copy of the
first Calculus exam
with
solutions.
For those interested in previous editions, here is a sample
Placement Exam (with the Calculus Exam as well),
from last year.
For those interested in even more practice, here is a sample
Algebra Placement Exam
and a sample
Calculus Placement Exam, culled
from previous exams.
My office is Ryerson 354, and
you can e-mail me at:
boller@math.uchicago.edu
Course assistants for Math Camp, with their e-mail addresses, are:
Jennifer Humensky,
jhumensk@uchicago.edu
Tana Johnson,
tana@uchicago.edu
Stephan Whitaker,
whitaker@uchicago.edu
The text for the course is "Applied Calculus," 9th Ed., by
Laurence D. Hoffman and Gerald L. Bradley, McGraw-Hill 2007,
ISBN 0-07-305192-6. 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.
Algebra and Pre-Calculus
Notes from Monday, August 27:
Axioms for the Real Numbers,
Number Systems
Suggested reading for August 27: Appendices A1 and A2 from the text
Suggested problem for August 27: Use the Axioms to prove the familiar
algebra formula for the difference of two squares: a^2-b^2=(a-b)(a+b)
Notes from Tuesday, August 28: Definitions and Theorems 1 (Algebra, Absolute Value,
Intervals).
Suggested problems for August 28: Problems 2.
Notes from Wednesday, August 29:
Definitions and Theorems 2 (Lines).
Suggested reading for August 29: Chapter 1, Sections 1.1-1.3
(Functions, Graphs, Linear Functions).
Suggested problems for August 29: Problems 3.
Notes from Thursday, August 30:
Definitions and Theorems 3 (Exponentials and Logarithms).
Suggested reading for August 30: Chapter 4, Sections 4.1-4.2 (Exponential
and Logarithmic Functions).
Suggested problems for August 30: Problems 4.
Calculus
Suggested reading for Tuesday, September 4: Sections 1.5 (Limits) and
2.1 (The Derivative).
Suggested problem for September 4: Use the technique from class to find the
derivative of f(x)=x^3.
Notes from Wednesday, September 5:
Definitions and Theorems 4 (Limits and Continuity).
Suggested reading for September 5: Sections 1.5 (Limits), 1.6 (One-Sided
Limits and Continuity) and 2.1 (The Derivative).
Suggested problems for September 5: Problems 6.
Notes from Thursday, September 6:
Definitions and Theorems 5 (Differentiation).
Suggested reading for September 6: Sections 2.2 (Techniques of
Differentiation) and 2.3 (Product and Quotient Rules).
Suggested problems for September 6: Problems 7.
Notes from Friday, September 7:
Definitions and Theorems 6 (Differentiation of Logs and Exps, Chain Rule). Now slightly updated!
Suggested reading for September 7: Sections 2.4 (The Chain Rule) and
4.3 (Differentiation of Logarithmic and Exponential Functions).
Suggested problems for September 7: Problems 8.
Suggested reading for September 10: Sections 2.6 (Implicit Differentiation
and Related Rates).
Suggested problems for September 10: Problems 9. Slightly downgraded.
Notes from Tuesday, September 11:
Definitions and Theorems 10 (Mean Value Theorem, Analysis of Functions).
Suggested reading for September 11 and 12:
Sections 3.1 (Increasing/Decreasing,
Relative Max/Min) and 3.2 (Concavity and Points of Inflection).
Suggested problems for September 11 and 12: Problems 10.
Suggested reading for September 12 and 13:
Sections 3.3 (Curve Sketching) and 3.4 (Optimization)
Notes from Thursday, September 13:
Definitions and Theorems 12 (Limits at Infinity, Infinite Limits, and Asymptotes).