RES-ECON 590ME: Mathematics for Economics and Business

Fall Semester 2026
Credits: 4
M,W,F 9:05-9:55 (In-Person)

Instructor: Prof. John M. Spraggon
Email: @email
Stockbridge 224
Office Hours: Tuesdays 9:30am- 10:30am, or by appointment.

Teaching Assistant: TBD
Office hours: TBD
Discussion section: TBD

Course Description: 

This course provides the mathematical foundation necessary for graduate study in economics and useful for many quantitatively-oriented business fields such as finance, management, and analytics. It covers differential and integral calculus, multivariable functions, vectors, and matrix algebra. The course emphasizes intuition, problem-solving, and connections between mathematics and economic reasoning, with applications that extend to business, finance, management, and other decision-focused disciplines.

Prerequisite: Math 127 or Math 131

Student Learning Objectives: 

By the end of this course, students will be able to:

• Differentiate and integrate functions of one and several variables, and use these tools to analyze and solve quantitative problems.
• Compute and interpret partial derivatives, gradients, and Hessians to identify and classify critical points of multivariable functions.
• Apply vector operations such as addition, scalar multiplication, dot products, and projections to represent and analyze geometric and analytical relationships.
• Perform matrix operations including addition, multiplication, inversion, and finding determinants, and use these tools to solve systems of linear equations.
• Construct and analyze linear models using vector and matrix notation, including expressing systems of equations compactly and interpreting their solutions.
• Develop analytical reasoning skills by selecting appropriate mathematical tools to solve problems and explain each step of the solution process clearly.
• Strengthen quantitative readiness for advanced coursework requiring a solid understanding of calculus, vectors, and linear algebra.

Course Materials: 

My intention is to provide detailed slides for all of the material, before the lectures.  As such, the textbooks below are valuable, but not required.  Additionally, I recommend Wolfram Alpha (https://www.wolframalpha.com/) to provide assistance with problem solving.

• Stewart, J., Clegg, D. K., & Watson, S. (2020). Calculus: Early transcendentals (9th ed.). Cengage Learning. 
• Lay, D. C., Lay, S. R., & McDonald, J. J. (2021). Linear Algebra and Its Applications (6^th ed.) Pearson.

AI Policy: 

AI is a valuable tool, and it is reasonable to expect that you will generally have access to it. That said, it is very important for you to understand how mathematics works, and be able to do it yourself.  The goal of the course is for you to understand the mathematics with the ultimate goal of being able to integrate your understanding of mathematics and economics.  To that end, the majority of your marks for this course will be earned by solving problems in person, either during the weekly quizzes, on the midterms or final.  So you can use AI to solve the assignment problems, but if you do not understand how to solve them yourself you will not do very well on the quizzes, midterm or final. My advice is to work in small groups on the assignments.  If you find that you can not do a particular problem as a group, then use Wolfram Alpha or another AI tool to find the solution.  But then figure out what the barrier was, and I am happy to discuss these barriers individually or in class.

Attendance Policy: 

Attendance is expected.  There will be weekly in class quizzes.  Please let me know if you will not be able to attend class.

Late/ Make-Up Work Policy: 

There will be a 1% grade reduction per day for any material handed in late.  If there is an issue and you know ahead of time you will not be able to submit something on time, let me know and we will determine the best way to proceed.

Grade Weight and Course Requirements:

• Quizzes – 10 % 
  • Quizzes are designed to keep students engaged with the material that is covered each week. These will be during the first part of the Friday class.
• Assignments- 20%
  • Homework are designed to reinforce and provide practice for the material covered in class. Due on Fridays, at the start of class each week. 
• Midterm Exam- 40%
  • 2 midterm exams to assess your understanding of the concepts. The midterm exam with the highest score is worth 25% and the other 15%. 
• Final Exam- 30%
  • The final exam is comprehensive and takes place during finals’ week.

Grading Scales: 

Note: Graduate students enrolled in 500-level courses cannot receive C-, D+, D; the lowest passing grade for a graduate student enrolled in a 500-level course is C.

Academic Honesty Policy:

UMass Amherst is strongly committed to academic integrity, which is defined as completing all academic work without cheating, lying, stealing, or receiving unauthorized assistance from any other person, or using any source of information not appropriately authorized or attributed. As a community, we hold each other accountable and support each other’s knowledge and understanding of academic integrity. Academic dishonesty is prohibited in all programs of the University and includes but is not limited to: Cheating, fabrication, plagiarism, lying, and facilitating dishonesty, via analogue and digital means. Sanctions may be imposed on any student who has committed or participated in an academic integrity infraction. Any person who has reason to believe that a student has committed an academic integrity infraction should bring such information to the attention of the appropriate course instructor as soon as possible. All students at the University of Massachusetts Amherst have read and acknowledged the Commitment to Academic Integrity and are knowingly responsible for completing all work with integrity and in accordance with the policy: (https://www.umass.edu/senate/book/academic-regulations-academic-integrity-policy)

Accommodations Statement:

The University of Massachusetts Amherst is committed to making reasonable, effective, and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services, meet with an Access Coordinator in Disability Services, and send your accommodation letter to your faculty. Information on services and registration is available on the Disability Services website (https://www.umass.edu/disability/)

Title IX Statement (Non-Responsible Employee):

In accordance with Title IX of the Education Amendments of 1972 that prohibits gender-based discrimination in educational settings that receive federal funds, the University of Massachusetts Amherst is committed to providing a safe learning environment for all students, free from all forms of discrimination, including sexual assault, sexual harassment, domestic violence, dating violence, stalking, and retaliation. This includes interactions in person or online through digital platforms and social media. Title IX also protects against discrimination on the basis of pregnancy, childbirth, false pregnancy, miscarriage, abortion, or related conditions, including recovery. There are resources here on campus to support you. A summary of the available Title IX resources (confidential and non-confidential) can be found at the following link: https://www.umass.edu/titleix/resources. You do not need to make a formal report to access them. If you need immediate support, you are not alone. Free and confidential support is available 24 hours a day / 7 days a week / 365 days a year at the SASA Hotline 413-545-0800.