Graduate & UG teaching

Teaching Undergraduate and Graduate Courses in Mathematics

I did conduct regular voluntary advanced mathematics  seminar for courses listed below.   Participants were from my alma mater NIT Allahabad and  Harish Chandra Research Institute.  

• An Introductions to Proofs - This course,  either in brief or in details, I teach to everyone whosoever participates in my seminar. This courses is completely need based and largely deals with art of proofs and applications of theorems of mathematics that have appeared in various mathematical contests - Berkley's Problems book in Mathematics, Polya's - How to solve it, Hungary Mathematics Contest, Stanford Mathematics Problem Book, IMO problems, University of Toronto Undergraduate Mathematics Competitions. 

• A rigorous foundational course in function of real variable (Participants : Dr. S. Manikandan, Samrat Kadge, Nitish Kumar, Ram Singh Yadav, Ujjwal Verma),

  • •  Terence Tao's Analysis I

    • Vladimir Zorich's Analysis I 

• Theory of continuous functions in normed linear and metric spaces (Participants : Dr. S. Manikandan, Samrat Kadge, Nitish Kumar, Yuri. R. Mikhyalov, Ujjwal Verma)  

  • • Elementary real Analysis in Metric Spaces, textbook Shilov's Elementary  Real and Complex Analysis  

    • Terence Tao's Analysis II 

    • Mathematical Analysis: Linear and Metric Structures and Continuity 

• Differential Calculus in Normed Linear  Spaces (Participants : Dr. S. Manikandan, Ph.D and Dr. Ebtsam H. Taha)

  • • A classical Book  Cours de calcul différentiel by french Mathematician Henri Paul Cartan 

    • A beautiful treatise on theory of differentiation in euclidean spaces entitled Multidimensional Real Analysis (I) by  Johannes Jisse (Hans) Duistermaat

    • Namely the chapter "differential calculus in Banach Spaces" from a beautiful book Foundation of Modern Analysis by Jean Dieudonne 

    • A standard material on subject of Differential Calculus in Topological Linear Spaces. This note sheds lot of light upon the various problems related to definition of derivative in different types of underlying spaces. One can think how to give definition of a derivative in spaces  with no notion of usual metric/distance function. 

    • One article of interest is Various Definitions of Derivatives in Linear Topological Spaces published in Russian mathematical survey. 

    • Two significant and perhaps first of theirs kind text are  Sternberg's & Loomis - Advanced Calculus and Steenrod, Spencer, Nickerson - Advanced Calculus. These two books shaped mathematical thought of many leading mathematicians. 

• An introduction to exterior algebra (Participants : Dr. S. Manikandan, Ph.D and Dr. Ebtsam H. Taha)

  • • First five chapters in Greub's Multilinear Algebra  

    •  Advanced Calculus   by  H.K Nickerson, D.C. Spencer, N.E. Steenrod 

• Group Theory, Ring Theory (Using Language of Category Theory) (Participants : Dr. S. Manikandan, Yuri. R. Mikhyalov, Ujjwal Verma.  Last two participants being MSc students from NIT Allahabad)

  • • Paolo Aluffi's Algebra  

• Ordinary Differential Equation - one of the most beautiful book on subject and written by  Russian mathematician and my mathematical hero V I arnold  . Participants (Participants : Dr. S. Manikandan)

• Manifolds, Tensor Analysis and Applications from a book with same title written by  Jerrold E. Marsden, Ralph Abraham, Tudor Ratiu. Marsden is my other mathematical hero and anything that he has written and researched upon is of very close interests to my scientific teaching and research.