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"While the rigorous mathematical coursework at Krea showed me that some questions are still unsolved, the techniques taught have made me optimistic while facing new problems. Engaging with the subtler aspects of the subject, such as its social, historical and philosophical dimensions has mainly been possible due to the supplemental coursework and the interactions with faculty and peers, and this has heavily influenced the way I think about, write and present mathematics."

Nayan Rajesh

Cohort of 2022
Future Dreams: I hope to use category theory and the principle of compositionality to study structure – mathematical and otherwise.

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Mathematics at Krea

Mathematics has been a fundamental domain of human thought, imagination, and creativity for thousands of years, across a variety of cultures. Today, mathematical concepts have not only applications in mathematics, but also across extraordinarily large number of disciplines, including the physical, natural, and social sciences; engineering; data science; business; and finance. The Krea University Mathematics Major serves as a comprehensive introduction to modern mathematical thought, and also provides training in mathematical problem-solving. It also motivates an understanding of the direction, fundamental relevance, applicability, and social context of mathematics in the 21st century.

The increasing importance of pure mathematics, as well as the use of algorithmic and statistical techniques across disciplines suggests that the relevance of mathematics will only grow. Students will be introduced to these domains and their applications, both within the classroom and through real-world immersive experiences, and will therefore be excellently placed to develop further specific and broad competencies in these areas.

Certain latest developments in areas like geometry, topology, algebra, analysis, number theory, combinatorics and partial differential equations increasingly impact many facets of human life. Mathematics students at Krea will be exposed to these developments through coursework and seminars.

The Approach

A student majoring in Mathematics at Krea will emerge with fluency in the language of mathematical and logical reasoning, and gain specific technical knowledge and understanding of a broad core of foundational content in areas such as calculus, algebra, analysis, probability, differential equations, geometry, topology, combinatorics  and number theory. They are able to also take a number of more specialised courses from a basket of recommended electives; this will deepen their understanding of specific mathematical disciplines in line with their interests. The topics selected for these recommended elective courses provide a snapshot of the breadth and depth of modern mathematics. Upon completion of their degree, a Krea mathematics major will be able to appreciate some of the questions and themes that guide current research in mathematics, and recognise the nature of the subject as a creative technical discipline.

The students will have the opportunity to study, through interdisciplinary coursework, how mathematics resonates and interacts with other academic areas. Students majoring in Mathematics at Krea will develop an appreciation for the historical context of the field. Writing and communicating mathematical information coherently and precisely is an important skill, involving appropriately framing context and describing technical details – in an increasingly interconnected and technologically dependent world it is also becoming important for technically and scientifically trained individuals to write effectively for a non-technical audience. The Mathematics Major at Krea will strongly emphasise the importance of good writing technique, and students majoring in Mathematics will be trained along these lines. Krea mathematics students, like their counterparts majoring in other disciplines, will write a Capstone thesis in their final year. This will provide an opportunity to develop a comprehensive understanding of a specific topic of interest; allow a hands-on appreciation for the nature of mathematical research; and offer a chance to further hone communication skills through long-form specialised writing.

Programme Details

Courses

Required courses for a 3-year Mathematics UG degree / 4-year Double Major in which Mathematics is a subject
1. Proofs and Ideas (MATH 191, 4 credits)
2. Analysis 1 (MATH 201, 4 credits)
3. Analysis 2 (MATH 202, 4 credits)
4. Analysis 3 (MATH 203, 4 credits)
5. Analysis 4 (MATH 304, 4 credits)
6. Complex Analysis (MATH 305, 4 credits)
7. Linear Algebra (MATH 230, 4 credits)
8. Algebra 1 (MATH 231, 4 credits)
9. Algebra 2 (MATH 232, 4 credits)
Any four of the following courses:
10. Topology 1 (MATH 341, 4 credits)
11. Complex Analysis (MATH 305, 4 credits)
12. Algebra 3 (MATH 333, 4 credits)
13. Probability (MATH 313, 4 credits)
14. Numerical Methods (MATH 328)
Required courses for a 3-year Double Major in which Mathematics is a subject
1. Proofs and Ideas (MATH 191, 4 credits)
2. Analysis 1 (MATH 201, 4 credits)
3. Analysis 2 (MATH 202, 4 credits)
4. Analysis 3 (MATH 203, 4 credits)
5. Analysis 4 (MATH 304, 4 credits)
6. Complex Analysis (MATH 305, 4 credits)
7. Linear Algebra (MATH 230, 4 credits)
8. Algebra 1 (MATH 231, 4 credits)
9. Algebra 2 (MATH 232, 4 credits)

 

Any three of the following courses:

10. Topology 1 (MATH 341, 4 credits)
11. Complex Analysis (MATH 305, 4 credits)
12. Algebra 3 (MATH 333, 4 credits)
13. Probability (MATH 313, 4 credits)
14. Numerical Methods (MATH 328)
Required courses for a Mathematics Minor in a 4-year UG degree / Mathematics Minor in a 3-year UG degree / Mathematics Concentration in a 4-year UG degree / Mathematics Concentration in a 3-year UG degree
1. Proofs and Ideas (MATH 191, 4 credits)
2. Analysis 1 (MATH 201, 4 credits)
3. Analysis 2 (MATH 202, 4 credits)
4. Linear Algebra (MATH 230, 4 credits)
Sample Electives (4-credit courses):
1. Fourier Analysis
2. Functional Analysis
3. Harmonic Analysis
4. Combinatorics
5. Algebraic Curves
6. Representation Theory
7. Number Theory
8. Geometric Group Theory
9. Algebraic Topology
10. Differential Topology
11. Differential Geometry
12. Mathematical Logic
13. Information Theory and Cryptography
14. Dynamical Aystems
Affiliated Required Courses
1. Writing and communication in mathematics (2 credits)
2. Computational methods in mathematics (2 credits)
3. Mathematics: a social history of ideas (1 credit)
4. Ethics in mathematics (1 credit)

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