SWIM@KSoM is an intensive instructional school in Mathematics planned at Kannur University (Thavakkara Campus) from May 05, 2025 to May 30, 2025. The workshop involves around 40 lectures on Analysis, Algebra and Linear Algebra, which are augmented by problem solving sessions. This workshop is intended for highly motivated BSc students entering into their third year. The lectures are given by experienced and well known mathematicians.
Note: This list is tentative and subject to confirmation.
| Date | Morning Session | Afternoon Session |
|---|---|---|
| May 5 (Mon) | Introduction to University Mathematics (E K Narayanan) |
Introduction to University Mathematics (Krishna Hanumanthu) |
| May 6 (Tue) | Introduction to University Mathematics (Krishna Hanumanthu) |
Introduction to University Mathematics (E K Narayanan) |
| May 7 (Wed) | Analysis (E K Narayanan) |
Linear Algebra (Krishna Hanumanthu) |
| May 8 (Thu) | Algebra (Anandavardhanan U K) |
Analysis (E K Narayanan) |
| May 9 (Fri) | Linear Algebra (Krishna Hanumanthu) |
Algebra (Anandavardhanan U K) |
| May 12 (Mon) | Analysis (Jayanthan A J) |
Linear Algebra |
| May 13 (Tue) | Analysis (Jayanthan A J) |
Algebra (K N Raghavan) |
| May 14 (Wed) | Algebra (K N Raghavan) |
Linear Algebra |
| May 15 (Thu) | Analysis (Jayanthan A J) |
Algebra (K N Raghavan) |
| May 16 (Fri) | Algebra (K N Raghavan) |
Linear Algebra |
| May 19 (Mon) | Analysis | Linear Algebra |
| May 20 (Tue) | Analysis | Algebra (R Venkatesh) |
| May 21 (Wed) | Linear Algebra | Analysis |
| May 22 (Thu) | Algebra (R Venkatesh) |
Linear Algebra |
| May 23 (Fri) | Analysis |
Algebra (R Venkatesh) |
| May 26 (Mon) | Linear Algebra (Divakaran D) |
Algebra (R Venkatesh) |
| May 27 (Tue) | Algebra (R Venkatesh) |
Linear Algebra (Divakaran D) |
| May 28 (Wed) | Analysis (Manjunath Krishnapur) |
Algebra (R Venkatesh) |
| May 29 (Thu) | Linear Algebra (Divakaran D) |
Analysis (Manjunath Krishnapur) |
| May 30 (Fri) | Analysis (Manjunath Krishnapur) |
Linear Algebra (Divakaran D) |
This introductory module covers fundamental concepts including the Natural Numbers, the Principle of Mathematical Induction, the Binomial Theorem, and an Introduction to Sets. It delves into the Algebra of Sets and the concept of Cardinality. Essential tools like Logical Notation, Relations, Equivalence Relations, and Functions are introduced. The module concludes with techniques for Handling Logical Notation, understanding Quantifiers, Constructing Mathematical Statements, developing Proofs, and general Problem Solving strategies.
Based on Tao's Analysis - I, this course covers foundational topics starting with the Natural Numbers and Set Theory, including functions, images, and cardinality. It then introduces the Integers and Rationals, Absolute Value, and the concept of gaps in rational numbers. A rigorous construction of the Real Numbers is presented, followed by the Axiom of Completeness and Limits of Sequences. The course explores Continuous Functions on R, covering Subsets of the Real Line, the Algebra of Continuous Functions, Limiting Values, properties of Continuous Functions, Monotonic Functions, and Uniform Continuity. Finally, the basics of Differentiation are covered, including definitions, Local Maxima/Minima, properties of Monotone Functions, the Inverse Function Theorem, and L'Hôpital's Rule.
Based on Artin's Algebra, this course begins with Matrix Operations, Row Reduction, the Matrix Transpose, Determinants, and Permutations. It then introduces fundamental algebraic structures, covering Laws of Composition, Groups and Subgroups, Subgroups of the Additive Group of Integers, Cyclic Groups, Homomorphisms, and Isomorphisms. Concepts like Equivalence Relations, Partitions, Cosets, Modular Arithmetic, the Correspondence Theorem, Product Groups, and Quotient Groups are explored. The course also touches upon Group Actions, including Cayley's Theorem, the Class Equation, and concludes with the Sylow Theorems.
Based on Artin's Algebra, this course covers core concepts of linear algebra. It starts with Subspaces of $\textbf{R}^{n}$ and introduces the concept of Fields. The definition and properties of Vector Spaces are discussed, followed by Bases and Dimension, techniques for Computing with Bases, and Direct Sums. The course then moves to Linear Operators, the Dimension Formula, and representing linear maps using the Matrix of a Linear Transformation. Key topics like Eigenvectors and Eigenvalues, the Characteristic Polynomial, and finding Triangular and Diagonal Forms are also covered.
Resources will be updated soon.