- 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? Information for placement within the calculus sequence is provided below. Your background and previous calculus experience will place you into the most suitable course.You may also contact a member of the Mathematics Department for advice.

**Contemporary Mathematics (MATH 130) (QA*)**- 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. Instructor consent is required to receive credit for MATH 130 after MATH 251 is completed.**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.**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.**Modeling with Calculus (MATH 140) (QA*)**– Modeling with Calculus introduces and applies the concept of calculus to solve open-ended, real-word problems, especially those in the natural and social sciences. The emphasis is on developing and interpreting mathematical models. Topics include differential calculus, linear algebra, and differential equations. This course takes advantage of computational tools so that the focus can be on calculus concepts useful in applied work. This course is appropriate for students with no prior calculus experience. 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 152, MATH 153, or MATH 249; see calculus placement advice below.**Accelerated Calculus I (MATH 151) (QA*)(0.5 cr)**- A first course in calculus for students with some previous exposure to the subject. Topics covered include limits; continuity; derivatives of algebraic, trigonometric, and exponential functions; implicit differentiation; the Mean Value Theorem; and optimization.**Accelerated Calculus II (MATH 152) (QA*)(0.5 cr)**- A second course in Calculus. Topics covered include definite and indefinite integrals, the Fundamental Theorem of Calculus, volume, arc length and surface areas, integration techniques, improper integrals, polar coordinates, and parametric equations. Prerequisites: MATH 140 or MATH 151, or equivalent.**Sequences and Series (MATH 153) (QA*)(0.5 cr)**- A half-semester course on sequences and series. Topics covered include sequences and series, Taylor Polynomials, Taylor Series, convergence, and Fourier Series. Prerequisite: MATH 152 or equivalent.**Multivariable Calculus (MATH 249) (QA*)**- Three-dimensional analytic geometry; partial differentiation; maxima-minima problems; multiple integrals; vector fields, curl and divergence; line and surface integrals; applications. Prerequisite: Prior calculus experience with integrals; see calculus placement advice below. Please note that MATH 249 does not cover information included in MATH 153 (Sequences and Series).*Passing MATH 249 with a C- or better satisfies both quantitative analysis requirements*.

### Calculus Placement Advice

In the Advising and Course Preferences Questionnaire, indicate if you have previous calculus experience. This data will assist the Registration Advisor in placing you into the most suitable course based on your background. While each specific situation is different, we generally follow the placement advice outlined below.Students with no calculus background should take MATH 140 Modeling with Calculus. This course is designed for students who are likely to only take one course in calculus. We recommend that students have high school math beyond Algebra II. Students with some exposure to calculus who are planning to take more than one calculus course should consider taking Accelerated Calculus I MATH 151, a 0.5 credit course.

Preparation for Calculus: In most cases, students who want to take calculus but who have not had calculus before should take MATH 140, which includes significant pre-calculus review. Students who feel they need more review also have the option to sign up for MATH 135 Preparation for Calculus. Please note that MATH 135 does not carry a QA or QA* designation. Please contact a member of the Math Department if you are not sure which course is best for you.

**Students with AP credit**:

**A score of 4 on the Calculus AB exam**earns credit for MATH 151 and places students into MATH 249, MATH 152, or MATH 153.**A score of 5 on the Calculus AB exam or a score of 4 on the Calculus BC exam**earns credit for MATH 151 and MATH 152, and places students into MATH 249.**A score of 5 on the Calculus BC exam**earns credit for MATH 151, MATH 152, and MATH 153 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 153 or MATH 249 |

Full year non-AP | A's | MATH 153 or MATH 249 |

Full year AP (A/B or B/C versions) | B's or B/C | MATH 152 |

Full year non-AP | A/B or B's | MATH 152 or MATH 153 |

Semester only or full year with lower grades | MATH 140 or MATH 151 |

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 140 or MATH 151. 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 151* & 152* or 153*, PHYS 221 & 222 |

Computer Science |
CS 141* & 241, MATH 152* and 153* |

Economics |
ECON 230*, MATH 140* (or equivalent) |

Exercise Science |
MATH 138* |

Mathematics |
MATH 253, CS 141* |

Physics |
PHYS 221 & 222, MATH 249* and 256 |

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. |