We expect our graduates to be conversant with mathematics and quantitative reasoning and to be able to apply quantitative reasoning to understand and solve everyday problems.  Formal reasoning and the formality of logic are central tools for decision-making in an uncertain world.  Thus two quantitative courses, selected from a broad list, are required for graduation.  You may wish to take one of them during your first semester.  This is particularly recommended if you think you will go on to major in a field of study which requires quantitative background, or if you have been in math courses during your senior year in high school and want to continue your work without interruption.

Of the two required quantitative courses, at least one will be intended to expand students' quantitative boundaries and provide skills necessary to interpret and apply mathematics.  Such courses are designated by the symbol (QA*).  The other course may include discipline-based applications of quantitative methodology, such as physics or computer science, or may be a mathematics or statistics course.  It will be designated by either (QA*) or (QA).

Majors requiring specific quantitative courses:

Major	Required
Biology	CHEM 116
Chemistry	CHEM 116, MATH 141* & 142*, PHYS 221 & 222
Computer Science	CS 231*, CS 241, MATH 142*, others.
Economics	ECON 230*, MATH 141* or equivalent
Exercise Science	MATH 138*
Mathematics	MATH 249*, CS 231*, others.
Physics	PHYS 221 & 222, MATH 249*, CS 231*, others.
Psychology	PSYC 252 & 253*
Sociology	SOC 301*
Graduate study - GRE exam	The quantitative portion of the GRE includes some calculus-based questions.
Pre-Med	Many medical schools require a course in Calculus.
Courses listed with a * are QA* courses, others are QA courses

Quantitative and Analytical Reasoning Courses Fall 2008

QA Courses (Star)
*CS 150  (1.0) Scientific Computing
*CS 231  (1.0) Introduction to Programming
ECON 230 (1.0) Economic Statistics  
MATH 130 (1.0) Contemporary Mathematics
MATH 138 (1.0) Statistics
MATH 141 (1.0) Calculus I                                    
MATH 142 (1.0) Calculus II                                   
MATH 249 (1.0) Multivariable Calculus                  

QA Courses (No Star)
*CS 130 (1.0) Computing Concepts
PHIL 140 (1.0) Symbolic Logic                                                   
*PHYS 221 (1.0) Introductory Physics I
*PHYS 222 (1.0) Introductory Physics II

MATHEMATICS PLACEMENT

Based on your previous coursework and experience in mathematics, you can determine which of the following initial mathematics courses would be most appropriate if you chose to take a Mathematics course to fulfill the Quantitative and Analytical Reasoning requirement.  Read the description of these courses carefully, mindful of your prior math preparation, and choose the level that matches your interests and abilities.  First-year students typically choose their first mathematics course from among the four options listed below.  Several majors require specific quantitative courses as seen in the table above.

Students who are primarily seeking to obtain a broad background and to fulfill the quantitative requirement will be best served by options 1-4.  Students desiring a more technical quantitative background, particularly for use in mathematics or quantitative science, will be better served by option 4-5, a course in the main calculus sequence.  Option 4 does indeed fit both categories of student.  All of the courses in options 1-4 have the (QA) or (QA*) designation as indicated

If you opt to take calculus, which course in the sequence is for you?  Advice for placement within the calculus sequence is provided below.  You may also contact a member of the Mathematics Department for advice – see http://www.willamette.edu/cla/math/faculty/.

1. Techniques of Mathematics (Math 130) (QA*) - A survey of selected applications of mathematics.  Topics may include: mathematics of voting; apportionment; efficient scheduling; growth in nature, populations and economics; symmetry; fractal geometry; probability.  This is NOT a remedial course.  Prerequisite: two years of high school algebra.

2. Statistics (Math 138) (QA*) - An introduction to descriptive and inferential statistics.  Emphasizes everyday applications and practical skills.  This course is an excellent preparation for dealing with the statistics one encounters every day in our society, and is particularly recommended for students who neither need nor desire a calculus background.  Prerequisite: two years of high school algebra.

3. Discrete Mathematics (Math 163) (QA*) – An introduction to basic techniques and modes of reasoning in combinatorial problem-solving. Topics will be chosen from combinatorial mathematics, logic and Boolean algebra, difference equations, graph theory and applied algebra.  Prerequisite: two years of high school algebra.  Note this course is offered only in spring semester.

4. Calculus 1 (Math 141) (QA*) – An introduction to the main tools of calculus, the derivative and the integral, applied to algebraic and exponential functions, with applications.  Focus on conceptual understanding.  Prerequisite: High school math beyond Algebra II recommended.  Students who have taken a full year of high school calculus should begin calculus study with Math 142 or Math 249; see calculus placement advice below.

5. Calculus 2 (Math 142) (QA*) - A second course in calculus: review of differential and integral calculus via trigonometric and logarithmic functions, techniques and applications of integration, polar coordinates and parametric equations, infinite series.  Prerequisite: Previous Calculus experience required; see calculus placement advice below.

Multivariable Calculus (Math 249) - Calculus of functions of more than one variable.  Prerequisite: Math 142 or the equivalent (such as: a year of AP or Community College Calculus taken as a high school student).  Students entering Math 249 should be able to differentiate and integrate functions commonly encountered in first-year calculus, including trigonometric and exponential functions, and should be able to use the derivative and the integral in common applications.

Calculus Placement Advice:

Students with AP credit:  A score of 4+ on the Calculus A/B exam or a 4 on the Calculus B/C exam earns credit for Math 141 and places students into Math 249 or Math 142.  A score of 5 of the Calculus B/C exam earns credit for Math 141 and 142 and places students into Math 249.

Students with high school calculus but no AP credit: 

Calculus taken	Grades	Place into
Full year AP (A/B or B/C versions)	A’s or A/B	Math 249
Full year non-AP	A’s	Math 249
Full year AP (A/B or B/C versions)	B’s or B/C	Math 142
Full year non-AP	A/B or B’s	Math 142
Semester only or full year with lower grades		Math 141

Students wishing to place lower than recommended in this table will need departmental approval.

Students with no high school calculus who wish to enter the calculus sequence should enroll in Math 141.  We recommend that they have high school math beyond Algebra II.

General Calculus Placement advice:  As a rule, we recommend that students aim high in their calculus placement.  If a student gets in over their head, we can help them change to a lower level course in the sequence.  If a student finds him/herself unchallenged after three weeks in a lower-level course, it is often too late to change to a higher level.  If in doubt, please contact the department personally. 

Contact info is available on our web page: http://www.willamette.edu/cla/math/faculty/