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.
Each morning session consists of a 1.5 hour lecture (09:30 AM - 11:00 AM), a break, and a 1.5 hour TA session (11:30 AM - 1:00 PM). The afternoon session follows a similar pattern: lecture (2:00 PM - 3:30 PM), break, and TA session (3:45 PM - 5:15 PM).
| Date | Morning Session | Afternoon Session | ||
|---|---|---|---|---|
| Lecture (09:30-11:00) | TA (11:30-1:00) | Lecture (2:00-3:30) | TA (3:45-5:15) | |
| May 5 (Mon) | Introduction to University Mathematics | Introduction to University Mathematics | ||
| E K Narayanan | TA: Renjith T. | Krishna Hanumanthu | TA: Gobinda Sau | |
| May 6 (Tue) | Introduction to University Mathematics | Introduction to University Mathematics | ||
| E K Narayanan | TA: Renjith T. | Krishna Hanumanthu | TA: Gobinda Sau | |
| May 7 (Wed) | Linear Algebra | Analysis | ||
| Krishna Hanumanthu | TA: Gobinda Sau | E K Narayanan | TA: Renjith T. | |
| May 8 (Thu) | Analysis | Algebra | ||
| E K Narayanan | TA: Renjith T. | Anandavardhanan U K | TA: Deepak Dileep | |
| May 9 (Fri) | Linear Algebra | Algebra | ||
| Krishna Hanumanthu | TA: Gobinda Sau | Anandavardhanan U K | TA: Deepak Dileep | |
| May 12 (Mon) | Analysis | Linear Algebra | ||
| Jayanthan A J | TA: Renjith T. | Sruthymurali | TA: Gobinda Sau | |
| May 13 (Tue) | Analysis | Linear Algebra | ||
| Jayanthan A J | TA: Renjith T. | Sruthymurali | TA: Gobinda Sau | |
| May 14 (Wed) | Analysis | Algebra | ||
| Jayanthan A J | TA: Renjith T. | K N Raghavan | TA: Deepak Dileep | |
| May 15 (Thu) | Algebra | Algebra | ||
| K N Raghavan | TA: Deepak Dileep | K N Raghavan | TA: Deepak Dileep | |
| May 16 (Fri) | Algebra | Linear Algebra | ||
| K N Raghavan | TA: Deepak Dileep | Sruthymurali | TA: Gobinda Sau | |
| May 19 (Mon) | Analysis | Algebra | ||
| Manjunath Krishnapur | TA: Renjith T. | R Venkatesh | TA: Deepak Dileep | |
| May 20 (Tue) | Algebra | Analysis | ||
| R Venkatesh | TA: Deepak Dileep | Manjunath Krishnapur | TA: Renjith T. | |
| May 21 (Wed) | Linear Algebra | Algebra | ||
| A. K. Vijayarajan | TA: Gobinda Sau | R Venkatesh | TA: Deepak Dileep | |
| May 22 (Thu) | Analysis | Linear Algebra | ||
| Manjunath Krishnapur | TA: Renjith T. | A. K. Vijayarajan | TA: Gobinda Sau | |
| May 23 (Fri) | Analysis | Linear Algebra | ||
| Manjunath Krishnapur | TA: Renjith T. | A. K. Vijayarajan | TA: Gobinda Sau | |
| May 26 (Mon) | Algebra | Algebra | ||
| R Venkatesh | TA: Deepak Dileep | R Venkatesh | TA: Deepak Dileep | |
| May 27 (Tue) | Algebra | Linear Algebra | ||
| R Venkatesh | TA: Deepak Dileep | Divakaran D | TA: Gobinda Sau | |
| May 28 (Wed) | Linear Algebra | Linear Algebra | ||
| Divakaran D | TA: Gobinda Sau | Divakaran D | TA: Gobinda Sau | |
| May 29 (Thu) | Analysis | Linear Algebra | ||
| Sanjay P K | TA: Anoop V. P. | Divakaran D | TA: Gobinda Sau | |
| May 30 (Fri) | Analysis | Analysis | ||
| Sanjay P K | TA: Anoop V. P. | Sanjay P K | TA: Anoop V. P. | |
This course, "Introduction to University Mathematics," offers a foundational exploration of essential mathematical concepts, starting with natural numbers, induction, and set theory, before building the number system from integers and rationals to the formal construction of real numbers. It introduces key ideas like relations, functions, and mathematical logic, concluding with a deep dive into the Axiom of Completeness and its significant implications for the properties of the real number line, ultimately aiming to establish a rigorous understanding of the fundamental structures and logic necessary for higher-level mathematics.
This lecture series provides a comprehensive introduction to real analysis, drawing on Terence Tao's Analysis I. Structured to build from foundational concepts to advanced theorems, it begins with the Axioms of Completeness and Least Upper Bound Property, exploring real number structure, sequences (convergence, limits, Cauchy sequences), and key results like Bolzano-Weierstrass. The series transitions to continuity (epsilon-delta definitions, Intermediate/Extreme Value Theorems), uniform continuity, and algebraic properties of continuous functions. Later lectures focus on differentiation (derivatives, Mean Value Theorem) and applications including Inverse Function Theorem and L’Hôpital’s Rule. Emphasizing rigorous proofs and central theorems, the series connects theoretical foundations with analytical tools, offering systematic progression from real numbers to function behavior while highlighting Tao's pedagogical approach.
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.
| Sl. No. | Application ID | Name |
|---|---|---|
| 1 | SWIM250423162135 | Balaji L |
| 2 | SWIM250407204728 | Alfa T |
| 3 | SWIM250425134832 | Lamiaa Mariyam B |
| 4 | SWIM250424094735 | Ranju Rajesh |
| 5 | SWIM250424164440 | Pavithra P M |
| 6 | SWIM250422134834 | Ninsha Ashokan Parakkandy |
| 7 | SWIM250425154415 | Sneha V N |
| 8 | SWIM250425173710 | Shabeeba VK |
| 9 | SWIM250424234341 | Midhuna K |
| 10 | SWIM250416162647 | Sanghamitra Sreekanth |
| 11 | SWIM250423171635 | Adithya Mohan N. |
| 12 | SWIM250417112823 | B. Sowmya |
| 13 | SWIM250420191540 | Abinav Kanhaa K |
| 14 | SWIM250422170101 | Rajil C R |
| 15 | SWIM250425134738 | Divya Lakshmi T |
| 16 | SWIM250424125907 | Hiba Fathima |
| 17 | SWIM250409221143 | Ashwin Deepak Cordeiro |
| 18 | SWIM250424165307 | Almas Fathima P |
| 19 | SWIM250425113040 | Angel Sreejith |
| 20 | SWIM250425000142 | Anuvind C |
| 21 | SWIM250426000331 | Dea Mary Denzil |
| 22 | SWIM250418103300 | M.N. Narendran |
| 23 | SWIM250425221226 | Nabeesathul Missriya |
| 24 | SWIM250424131217 | Afna Salim P |
| 25 | SWIM250414092244 | Bibiya Mary Kurian |
| 26 | SWIM250414121857 | Anuvidhya Shaji |
| Sl. No. | Application ID | Name |
|---|---|---|
| 1 | SWIM250411143224 | Rasina C |
| 2 | SWIM250424221233 | Arya K |
| 3 | SWIM250424221139 | Jeevana S S |
| 4 | SWIM250424220233 | Alok K P |
| 5 | SWIM250424183107 | Shana KC |
| 6 | SWIM250425151053 | Hina Akbar |
| 7 | SWIM250425162831 | Shalabha Chandran K |
| 8 | SWIM250424191448 | Fathimathul Sahala K N |
| 9 | SWIM250425164115 | Ananya K V |
| 10 | SWIM250425135940 | Karthika KV |
| 11 | SWIM250424110032 | Sneha K |
| 12 | SWIM250424162607 | Asnin Shan |
| 13 | SWIM250424192209 | Adithya K |