- Willamette
- College of Liberal Arts
- Office of the Dean
- Transfer Student Advising Manual
- Quantitative and Analytical Reasoning Courses

# Quantitative and Analytical Reasoning Courses

Formal reasoning and the formality of logic are central tools for decision-making in an uncertain world, and 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. Two quantitative courses are required for graduation (unless you successfully complete MATH 249). At least one of these credits will be intended to expand students' quantitative boundaries by providing the skills necessary to interpret and apply mathematics. Such courses are designated by the symbol (QA*) in the course schedule. The other course may be another (QA*) course or could be a discipline-based application of quantitative methodology, such as physics or computer science and is designated (QA). A list of fall courses that satisfy the quantitative requirement can be found in the 'Course Types' section of the Course Schedule.

Consult your Degree Audit to determine if you have fulfilled one or both of the quantitative requirements. If you have not already satisfied the quantitative requirement, you may wish to take one of your quantitative courses during your first semester. This is particularly recommended if you think you will go on to major in a field of study which requires a quantitative background.

### Mathematics Placement

If you have not completed the quantitative requirement and elect to take a quantitative course in your first semester you will need to choose the right course for you. Based on your previous coursework and experience in mathematics, you can determine which of the following initial mathematics/quantitative courses would be most appropriate. The quantitative courses listed below have the QA* designation. Read the description of these courses carefully, mindful of your prior math preparation, and choose the level that matches your interests and abilities. A list of specific quantitative requirements for various majors is given below.

**NOTE:** Options 1 – 3 (below) have no particular prerequisites beyond algebra 2. Any of these courses would be appropriate for students who are primarily seeking to obtain a broad background and to fulfill the quantitative requirement. Students desiring a more technical quantitative background, particularly for use in mathematics or quantitative science, should plan to take courses in the calculus sequence (Calculus 1, Calculus 2, and Multivariable Calculus, options 3 – 5 below). Completing multivariable calculus MATH 249 successfully will satisfy both quantitative requirements.

If you opt to enter the calculus sequence, where should you begin? Advice for placement within the calculus sequence is provided below. You may also contact a member of the Mathematics Department for advice.

- Contemporary Mathematics (MATH 130) - A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, growth and decay in nature and economics, symmetry and fractal geometry, probability and statistics. This is NOT a remedial course. Prerequisite: two years of high school algebra.
- Statistics (MATH 138) - An introduction to descriptive and inferential statistics. Emphasizes everyday applications and practical skills. This course is particularly recommended for students who neither need nor desire a calculus background, and is an excellent preparation for dealing with the statistics one encounters every day in our society. Prerequisite: two years of high school algebra.

### The Calculus sequence

- Calculus 1 (Math 141) – A first course in calculus which serves two purposes: 1 – a survey of calculus for those who want to know what calculus is "all about," but don’t intend to take any more mathematics, or 2 – the first course in calculus which prepares the student to continue to Calculus 2. Topics include the differential and integral calculus of algebraic and exponential functions, together with their applications. Students who have taken a full year of high school calculus should begin calculus study with MATH 142 or MATH 249.
- Calculus 2 (MATH 142) - Further study of differential and integral calculus including applications of integration, polar coordinates, parametric equations, infinite series, and an introduction to differential equations. Prerequisite: a calculus course.
- Multivariable Calculus (MATH 249) - Calculus of functions of more than one variable. Prerequisite: MATH 142 or the equivalent (such as: a full year of Advanced Placement Calculus or a year of junior 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.

### Some majors require specific quantitative courses:

Major |
Required |

Biology |
CHEM 116 |

Chemistry |
CHEM 116, MATH 141* & 142*, PHYS 221 & 222 |

Computer Science |
CS 141* & 241, MATH 142*, others |

Economics |
ECON 230*, MATH 141* |

Exercise Science |
MATH 138* |

Mathematics |
MATH 249* & 253 |

Physics |
PHYS 221 & 222, MATH 249* |

Psychology |
PSYC 252 & 253*, |

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. Some require two. Others require Statistics (Math 138*). Check with the pre-med advisor. |