• Quantitative Reasoning: Practical Math
• Quantitative Reasoning: Math for Everyday Use
• Quantitative Reasoning: Mathematics and the Greeks
• College Algebra
• College Algebra I
• College Algebra II
• Precalculus
• Introduction to the Calculus A
• Introduction to the Calculus B and Differential Equations
• Multivariable Calculus
• Linear Algebra
• Discrete Mathematics with Computer Science Applications
• Experimental Mathematics
• Quantitative Reasoning Examination

Students contemplating enrolling in the following mathematics courses--MATH E-3, E-5, E-6, E-8a, E-8b, E-8, E-10, E-15, E-16, or E-104--must complete a placement test before registering, unless in the preceding term they satisfactorily completed at Harvard Extension School the prerequisite qualifying course. Students who do not demonstrate a working knowledge of the prerequisites for a course when they take the placement test will have trouble keeping up with the course.

Placement Test Schedule

Fall term

Tuesday, August 18, 7:30-10 pm Science Center C

Wednesday, September 9, 7:30-10 pm Science Center D

Spring term

Wednesday, January 13, 7:30-10 pm Science Center C

Wednesday, January 27, 7:30-10 pm Science Center C

Students may start the placement test any time up to 9 pm. A late placement test will be administered from 7:30 to 10 pm on Friday, September 18, and Friday, February 5 in Science Center A.

The test takes about 11/4 hours to complete and has five sections covering the arithmetic operations, algebra, functions and graphing, logarithms, and trigonometry. Students are not expected to have studied for the test; placement will be made assuming students have not taken a mathematics course recently. In addition, every student who takes the examination will be available to register for a course, there is no minimum background required. Advice will be available at the testing sessions, and placement results will be available as soon as each student has finished the test. The placement advice should be followed carefully, as no review of prerequisites will be provided during the semester.

MATH E-3 through E-21b are under the supervision of Deborah Hughes Hallett, MA, Professor of the Practice in the Teaching of Mathematics, Harvard University. MATH E-8a, E-8b, and E-8 are algebra courses that are prerequisite to MATH E-10, which is a prerequisite to calculus. Students who do not intend to take precalculus may wish to take MATH E-3 or E-5 which introduce the personal computer, probability, and statistics, with applications to the social sciences.

For students in MATH E-3, E-5, E-6, E-8a, E-8b, E-8, E-10, E-15, and E-16, individual help will be available at the Question Center. The Center will be open Mondays, 5:30 to 7:30 pm, and Tuesdays, 7:35-9:35 pm in Sever Hall 307. The Math Question Center opens the second week of classes each term.

MATH E-3 Quantitative Reasoning: Practical Math
4 units. Undergraduate credit $545. Prerequisite(s): students must take the placement test.

Review of basic arithmetical procedures. An introduction to the interpretation of numerical data and to the use of the Macintosh personal computer. Graph reading and some statistical ideas, including sampling, testing a hypothesis, and constructing a confidence interval; correlation and regression. The course introduces students to the use of software packages, including a spreadsheet, but does not involve programming. New material will be presented during Tuesday classes; Thursdays will be reserved for review, individual help, and hands-on experience with the computer. All exams are given on Thursdays.

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MATH E-5 Quantitative Reasoning: Math for Everyday Use (10428)
Peter J. Martin, MS, Instructor, Newton North High School.
4 units. Undergraduate credit $545. Tuesday 7:35-9:35 pm. Sever Hall 213. Sections Tuesday 6:30-7:30 pm. Prerequisite(s): a satisfactory placement test score. Fall term.

Covers the same material as MATH E-3, but in greater depth and without the arithmetic review. This course is intended for students with no previous experience with computers or statistics, but with a solid command of arithmetic. However, algebra is not a prerequisite.

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MATH E-6 Quantitative Reasoning: Mathematics and the Greeks (21341)
Graeme D. Bird, PhD, Preceptor in Quantitative Reasoning in the Core Program, Harvard University.
4 units. Undergraduate credit $470. Tuesday 7:35-9:35 pm. Boylston Hall 103. Sections Tuesday 6:30-7:30 pm, Boylston Hall 103, beginning Feb. 9. Prerequisite(s): a good knowledge of algebra, which can be demonstrated either by a grade of A- or better in MATH E-8b or MATH E-8, or by a satisfactory placement test score. Spring term.

The legacy of the Greek mathematicians has been described as "one of the most stupendous achievements in the history of human thought." The Pythagorean theorem, Euclidean geometry, and Archimedes' spiral are but three examples of this legacy. In this course we will read brief extracts (in translation) from original mathematical works, and then work through a selection of problems. Weekly assignments will include some reading, but the emphasis will be on problem solving, both constructing geometrical figures and writing proofs of arguments. Needless to say, calculators will not be used, but rather the basic ancient Greek instruments: pencil, compass, and straightedge.

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MATH E-8 College Algebra
4 units. Undergraduate credit $470. Prerequisite(s): students must take the placement test.

This course covers the material in MATH E-8a and E-8b. It is intended for students who place into E-8a but who want to take E-10 the following term.

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MATH E-8a College Algebra I (10429)
David S. Abbruzzese, BS, Teaching Assistant in Physics, Harvard University.
2 units. Undergraduate credit $350. Wednesday 7:35-9:05 pm. Sever Hall 308. Sections Wednesday 6:30-7:30 pm, Sever Hall 308, beginning Sept. 23. Prerequisite(s): students must take the placement test. Fall term.

Review of arithmetic. Algebraic expressions and equations, and their manipulation and use in problem solving.

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MATH E-8b College Algebra II (20392)
David S. Abbruzzese, BS, Teaching Assistant in Physics, Harvard University.
2 units. Undergraduate credit $350. Tuesday 7:35-9:05 pm. Sever Hall 209. Sections Tuesday 6:30-7:30 pm, Sever Hall 101, beginning Feb. 9. Prerequisite(s): MATH E-8a or a satisfactory placement test score. Spring term.

Further work with algebraic expressions and equations; word problems; introduction to inequalities, absolute values, and graphing.

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MATH E-10 Precalculus
4 units. Undergraduate credit $470. Prerequisite(s): an A-minus grade in MATH E-8b or E-8, or a satisfactory placement test score.

An intensive course for students with superior algebra skills who want to enroll in MATH E-15 the following term. Requires the use of a graphing calculator (preferably the Texas Instruments TI-82).

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MATH E-15 Introduction to the Calculus A
4 units. Undergraduate credit $470. Prerequisite(s): MATH E-10 or satisfactory placement test score. Students must have an excellent working knowledge of algebra and the trigonometric and logarithmic functions.

Derivatives, graphing, optimization, and estimation. Algebraic, trigonometric, logarithmic, and exponential functions. An introduction to integration. Covers most of the topics in a first-semester calculus course, but with an emphasis on graphical and numerical work. Requires the use of a graphing calculator (preferably the Texas Instruments TI-82).

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MATH E-16 Introduction to the Calculus B and Differential Equations
4 units. Undergraduate credit $470. Prerequisite(s): MATH E-15 or equivalent--in other words, an excellent working knowledge of first-semester calculus, including the trigonometric and logarithmic functions.

Integration and differential equations, with applications. Covers most of the topics in a second-semester calculus course, but with an emphasis on graphical and numerical work. Requires the use of a graphing calculator (preferably the Texas Instruments TI-82).

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MATH E-21a Multivariable Calculus (20394)
Ted Pyne, PhD, Teaching Assistant in Physics, Harvard University.
4 units. Undergraduate credit $470. Thursday 5:30-7:30 pm. Sever Hall 306. Sections Tuesday 7:35-8:35 pm, Sever Hall 101, beginning Feb. 9. Prerequisite(s): MATH E-16 or equivalent. Spring term.

Vectors and matrices; vector-valued functions of many variables; partial derivatives; Taylor's theorem; optimization of functions of more than one variable; constrained extrema and Lagrange multipliers; multiple integration; line and surface integrals and Stokes's theorem.

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MATH E-21b Linear Algebra (10438)
Ted Pyne, PhD, Teaching Assistant in Physics, Harvard University.
4 units. Undergraduate credit $470. Thursday 5:30-7:30 pm. Sever Hall 102. Sections Monday 7:35-8:35 pm, Sever Hall 207, beginning Sept. 21. Prerequisite(s): MATH E-16 or equivalent. Fall term.

This course is designed for students who wish to pursue a career in various fields where applications of mathematical concepts are required or desirable. We will start with the solution of systems of linear equations as the basic concept of linear algebra. Subsequent topics will include the properties of vectors and matrices, matrix inversion, determinants, eigenvalues, and eigenvectors. There will be an emphasis on applications, including linear programming, the simplex algorithm, differential equations, and linear regression. Numerical methods for determining eigenvalues and eigenvectors will be introduced, and the method will be applied to the analytical hierarchy process for decision making.

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MATH E-104 Discrete Mathematics with Computer Science Applications (11478)
Thomas Koshy, PhD, Professor of Mathematics, Framingham State College.
4 units. Graduate credit $1,180. Thursday 5:30-7:30 pm. Science Center B-09. Sections to be arranged. Prerequisite(s): a good working knowledge of C++ or other structured language and of precalculus mathematics as evidenced by an appropriate score on the placement test; additional background in computing or in college-level mathematics is desirable, but not essential. Fall term.

An introduction to topics in discrete mathematics that are useful in computer science: mathematical logic, set theory, induction, recursion, combinatorics, relations and functions, and graphs. Includes an introduction to algorithm analysis and techniques for proving correctness of programs. Practical programming examples, as well as proofs of relevant theorems, will be discussed. The course is intended both for beginning students of computer science and for computer professionals.

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MATH E-110 Experimental Mathematics (11479)
Frank Purcell, PhD, Instructor, Concord Academy.
4 units. Undergraduate credit and graduate credit $1,180. Thursday 7:35-9:35 pm. 53a Church Street 2. Prerequisite(s): MATH E-10; a solid background in basic algebra including linear and quadratic function, exponents and radicals, and solving linear equations. Limited enrollment. Fall term.

This laboratory course uses the computer as a visualization tool to explore interesting areas of precalculus mathematics including functions and their graphs, parametric curves, complex numbers, probability distributions, recursive sequences, and matrix arithmetic. Each topic will be introduced through numerical and graphical experiments conducted in a simple computer algebra environment. The focus will be on developing mathematical intuition and problem-solving through concrete applications. Lab projects will include modeling with functions, drawing and animating curves and shapes, simulating random processes, and simple image processing. The course will be of special interest to teachers of high school mathematics who plan to integrate technology into their curriculum.

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QRR E-Exam Quantitative Reasoning Examination
Noncredit $60. Registration and withdrawal deadline: September 8 (fall term), January 21 (spring term).

Designed for ALB candidates who want to fulfill the data component of the quantitative reasoning requirement and for ALM candidates in biology and psychology who want to fulfill the statistics requirement by taking the exam, which is administered at the third class meeting. All the topics in MATH E-3, and E-5 are reviewed, but in a very accelerated format. Participants are assumed already to be familiar with the material by having worked through the QRR data book. The course should only be taken by students with strong math backgrounds and willingness to do some independent study. The course does not include the computer topics necessary to pass the computer component of the quantitative reasoning requirement (basic familiarity with word processing, spreadsheets, and graphics). The computer test will be administered at the last class meeting. For more information, students should call Graeme Bird at (617) 496-5143.

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