Foundations for Calculus and Advanced Topics
This two-week course reviews and strengthens the foundational calculus skills needed for success in college-level calculus, while introducing advanced mathematical concepts and computational tools. Each class combines lectures, collaborative problem-solving, and hands-on activities.
The course begins with a brief review of essential algebra and trigonometry, then progresses through core calculus topics, including limits, continuity, derivatives, integrals, infinite series, and polar coordinates, as well as multivariable calculus topics such as partial derivatives and multiple integrals. The second part of the course emphasizes real-world applications, and computational tools, including numerical methods, mathematical modeling, linear algebra and differential equations.
Afternoon sessions provide time for exercises, small group work, and guided discussions, helping students strengthen their foundations, build confidence, and prepare for college-level STEM coursework.
Students will:
- Strengthen foundational calculus skills, including limits, continuity, derivatives, integrals, and multivariable calculus topics, for a strong preparation for college-level mathematics.
- Develop computational proficiency by using computational tools to model problems, perform calculations, solve problems and implement numerical methods.
- Apply calculus to real-world applications, including solving differential equations and exploring mathematical models.
- Enhance problem-solving and critical thinking skills.
- Communicate mathematical ideas effectively, both orally and in writing, to build confidence and solid preparation for advanced STEM coursework
This course is offered at the UMass Charles River Campus with commuter and residential options available.
- Lectures and demonstrations of math topics and computational tools
- Exercises
- Small group work
- Guided discussions
Final Project: Students will give a final presentation on a mathematical topic of their choice.
Pre-Requisites
- Some prior knowledge of algebra and trigonometry is recommended
Materials
Students should bring:
- A notebook and pens/pencils
- A laptop or tablet (optional)
By the end of the course, students will be able to:
- Demonstrate mastery of foundational precalculus and calculus concepts, including limits, continuity, derivatives, and integrals.
- Apply multivariable calculus concepts, such as partial derivatives and multiple integrals, to solve problems.
- Use Python and computational tools to solve problems, perform calculations, and apply numerical methods.
- Solve ordinary differential equations and real-world problems using calculus and mathematical modeling.
- Communicate mathematical concepts clearly, both orally and in writing.
Class time is Monday-Friday from 9 am - 4 pm.
|
Time |
Activity |
|
9:00 AM–10:30 AM |
Lecture: Review of algebra and trigonometry; limits, continuity, derivatives, application problems, |
|
10:30 AM–10:40 AM |
Short Break |
|
10:40 PM–1:00 PM |
Lecture: Review of algebra and trigonometry; limits, continuity, derivatives, application problems, |
|
1:00 PM–2:00 PM |
Lunch Break |
|
2:00 PM–3:00 PM |
Activity: Class exercises, small group work, collaborative discussions, and hands-on activities |
| 3:30 PM–3:40 PM |
Short Break |
| 3:40 PM–4:00 PM |
Activity (continued) |
In the evenings and on weekends resident counselors will run a series of social activities. Students are encouraged to join in, relax and have fun with new friends! With social events on campus and in the city of Boston, and access to the Athletic Center, there's something for everyone to enjoy.
Learn more about student life at UMass Amherst Summer Pre-College
Meet the Faculty
Maria Correia, Senior Lecturer, Department of Mathematics & Statistics
Maria Correia is a Senior Lecturer in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. She teaches undergraduate courses including Calculus, Linear Algebra, Introduction to Scientific Computing, and Ordinary Differential Equations. Dr. Correia earned her Ph.D. in Mathematics from the University of Evora and is deeply committed to innovative, excellent, and inclusive teaching. She is a finalist for the 2025-2026 Distinguished Teaching Award. Her research interests include dynamical systems, differential equations, and numerical analysis.
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