# Options in Mathematics, Short Course

• Anytime
• Unavailable
Duration
University rank #1 (ARWU)
Harvard Summer School offers several open-enrollment courses, specialized in Mathematics, such as ''Mathematical Games and the Mathematical Process'', ''Groups and Symmetry" and "Vectors: a Tool for Teaching Algebra, Geometry, and Trigonometry''.

Please note, that the content, schedule, delivery format, availability and costs of Summer School Courses in Mathematics may be subject to change.

For the most up to date information, please visit the Harvard Summer School’s course options website.

###### Mathematical Games and the Mathematical Process

Games are considered a lighthearted pursuit, but behind many of them lies the wonderful and sometimes serious business of mathematics. Economists study game theory because of its application to many real world situations. This course explores the theory of mathematical games as an accessible way to expose young students to the mathematical process: exploring mathematical structures, analyzing patterns and conjecturing, making and critiquing arguments. We play and analyze many games and enthusiastically dive into the mathematics (algorithms, combinatorics, algebra, topology) that these reveal to us.

###### Groups and Symmetry

Symmetry is a notion that is fundamental to all of mathematics, and the right tool for describing symmetry is group theory. In this course, we take a hands-on approach to studying the symmetries of objects, especially those from elementary 2- and 3-dimensional geometry, and we use these as an opportunity to delve into the rich structures of finite groups. In particular, we realize the rotation groups of regular polygons and polyhedra as special subgroups of the symmetric on n elements.

###### Vectors: a Tool for Teaching Algebra, Geometry, and Trigonometry

Vectors are introduced, then applied to a variety of problems that cover almost the entire spectrum of high school mathematics: solving systems of linear equations, proving theorems of plane geometry, deriving trigonometric identities, and describing motion in two dimensions. This course helps teachers see how the use of vectors can provide a powerful way of connecting many various parts of the high school math curriculum for their students.

###### Registration opens March 1, 2017 for the following three summer sessions:
• Seven-week session: June 17–August 5, 2017
• Three-week session I: June 17–July 7, 2017
• Three-week session II: July 9–July 28, 2017

## Detailed Programme Facts

• Programme intensity Full-time
• Credits
4 alternative credits
• Languages
• English
• Delivery mode
On Campus

## Programme Structure

Please note, that the content, schedule, delivery format, availability and costs of Summer School Courses in Mathematics may be subject to change.

For the most up to date information, please visit the Harvard Summer School’s program website.

###### For instance, you can take the following courses:
• Introductory Functions with Modeling
• Precalculus Mathematics
• Calculus I
• Calculus I and II
• Calculus II
• Multivariable Calculus
• Linear Algebra and Differential Equations
• Spaces, Mappings, and Mathematical Structures (With An Introduction to Proof)
• Inquiries into Probability and Statistics
• Mathematical Games and the Mathematical Process
• Groups and Symmetry
• Real Analysis for Calculus Teachers
• Vectors: a Tool for Teaching Algebra, Geometry, and Trigonometry
• Teaching Projects: Math for Teaching Capstone Course

## English Language Requirements

You only need to take one of these language tests:

• Minimum required score:

100

The TOEFL iBT ® measures your English-language abilities in an academic setting. The test has four sections (reading, listening, speaking, and writing), each with a score range of 0-30, for a total score range of 0-120. Read more about TOEFL iBT ®.

Schedule TOEFL®
• Minimum required score:

600

The TOEFL®PBT is administered in a paper format and measures your ability to use and understand English in a classroom setting at the college or university level. It accurately measures how well you can listen, read and write in English while performing academic tasks. Read more about TOEFL®PBT.

Schedule TOEFL®
• Minimum required score:

7

The IELTS – or the International English Language Test System – tests your English-language abilities (writing, listening, speaking, and reading) on a scale of 1.00–9.00. The minimum IELTS score requirement refers to which Overall Band Score you received, which is your combined average score. Read more about IELTS.

Study abroad program directors look for mature, academically motivated students who are willing to broaden their horizons, experience a challenge, and grow as a person.

###### Who can apply

Harvard study abroad programs are selective. To apply, students must:

• Be at least 18 years old
• Have completed at least one year of college or be a first-year student
• Be in good academic standing

All programs are limited enrollment.

###### How to apply

For all programs, application requires a completed online application, including a statement of interest in the program, a nonrefundable \$50 application fee, and a transcript. Some programs may require additional application materials and interviews.

###### English Language Requirements

English is the language of instruction at Harvard Summer School. If your native language is not English, you must provide proof of English proficiency, unless you are an admitted degree candidate in Harvard College, the Harvard Extension School, or a Harvard graduate or professional school.

###### Visa Requirements

The F-1 student visa is the appropriate visa for you if your main reason for coming to the United States is to attend a Harvard Summer School session on campus.

To be issued the F-1 student visa, you must first obtain the I-20 Certificate of Eligibility from Harvard Summer School.

## Tuition Fee

• ### International Applies to you

3050 USD/full
Tuition Fee
Based on the original amount of 3050 USD for the full programme and a duration of  .
• ### National Applies to you

3050 USD/full
Tuition Fee
Based on the original amount of 3050 USD for the full programme and a duration of  .
We've labeled the tuition fee that applies to you because we think you are from and prefer over other currencies.
Tuition fee:
• 3050 USD 4 credit course
• 6100 USD 8 credit course

## Living costs for Cambridge

• 1814 - 3760 USD/month
Living Costs

The living costs include the total expenses per month, covering accommodation, public transportation, utilities (electricity, internet), books and groceries.

## Funding

StudyPortals Tip: Students can search online for independent or external scholarships that can help fund their studies. Check the scholarships to see whether you are eligible to apply. Many scholarships are either merit-based or needs-based.

### The Global Study Awards: get funded with up to £10,000 to study abroad

Together with the ISIC Association and British Council IELTS, Studyportals offers you the chance to receive up to £10000 to expand your horizon and study abroad. We want to ultimately encourage you to study abroad in order to experience and explore new countries, cultures and languages.