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Overview
What are the theoretical limits of computing power? What problems can be solved with computers? Which ones cannot? And how can we reason about the answers to these questions with mathematical certainty? Find out with this Mathematical Foundations of Computing course offered through Stanford University - Summer Sessions.
Outcomes
- At the completion of the course, students will feel comfortable writing mathematical proofs, reasoning about discrete structures, reading and writing statements in first-order logic, and working with mathematical models of computing devices.
- Throughout the course, students will gain exposure to some of the most exciting mathematical and philosophical ideas of the late nineteenth and twentieth centuries.
Programme Structure
Specific topics covered include:
- formal mathematical proofwriting
- propositional and first-order logic
- set theory
- binary relations
- functions (injections, surjections, and bijections)
- cardinality
- basic graph theory
- the pigeonhole principle
- mathematical induction
- finite automata
- regular expressions
- the Myhill-Nerode theorem
- context-free grammars
- Turing machines
- decidable and recognizable languages
- self-reference and undecidability
- verifiers
- the P versus NP question
Key information
Duration
- Full-time
- 2 months
Start dates & application deadlines
- Starting
- Apply before
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Language
English
TOEFL® IBT 100
Credits
5 SCH
Delivered
On Campus
Disciplines
Mathematics Computer Sciences View 63 other Short Courses in Mathematics in United StatesAcademic requirements
We are not aware of any specific GRE, GMAT or GPA grading score requirements for this programme.
English requirements
TOEFL® IBT 100
Student insurance
Make sure to cover your health, travel, and stay while studying abroad. Even global coverages can miss important items, so make sure your student insurance ticks all the following:
- Additional medical costs (i.e. dental)
- Repatriation, if something happens to you or your family
- Liability
- Home contents and baggage
- Accidents
- Legal aid
We partnered with Aon to provide you with the best affordable student insurance, for a carefree experience away from home.
Get your student insurance nowStarting from €0.53/day, free cancellation any time.
Remember, countries and universities may have specific insurance requirements. To learn more about how student insurance work at Stanford University - Summer Sessions and/or in United States, please visit Student Insurance Portal.
Other requirements
General requirements
To be eligible to apply, you must:
- Be at least 18 years of age by the start of the program.
- Have graduated from high school or secondary school or equivalent.
- Be a current university student or have some university or post-secondary experience.
Tuition Fee
To always see correct tuition fees
-
International
6860 USD/fullTuition FeeBased on the tuition of 6860 USD for the full programme during 2 months. -
National
6860 USD/fullTuition FeeBased on the tuition of 6860 USD for the full programme during 2 months. -
In-State
6860 USD/fullTuition FeeBased on the tuition of 6860 USD for the full programme during 2 months.
Living costs for Stanford
1100 - 1600 USD /month
Living costs
The living costs include the total expenses per month, covering accommodation, public transportation, utilities (electricity, internet), books and groceries.
Funding
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