Older school projects

current vita

The Synthesis Of Carvone I sem 1993-94 BITS Pialni
TIC projects are campus based R&D projects done in collaboration with professionals from various industries. This particular project was aimed at developing a process route for the synthesis of an organic chemical (Carvone) which would later be scaled up for industrial production.
Chaos And Turbulence I sem 1993-94 BITS Pialni
Turbulence was approached as one of the unsolved problems of theoretical physics. The current theories were reviewed as were similarities and differences with dynamical systems in routes to chaos and turbulence. In particular, the theories of Landau and Kolmogorov were reviewed. This project was done under the guidance of the Chemical Engineering Faculty.
With the view of assisting computer simulations an interpreted language for mathematical computation and primitive graphics was developed and implemented on the Linux operating system for i386 processors.
Chaotic Dynamical Systems II sem 1993-94 BITS Pialni
The mathematical theory of discrete dynamical systems, as developed by Devaney, was studied. The aim of this project was to develop the background and rigour required for further studies. Specific topics included: One dimensional iterative maps; the Logistic equation; critical points; hyperbolicity; Cantor sets; topological transitivity; definitions of chaos; symbolic dynamics; structural stability; Sarkovskii's theorem; Bifurcation theory;
As a brief excursion, Self Organized Criticality was also studied as a related (but distinct) phenomenon. Cellular Automaton models of sandpiles were attempted.
Quantum Mechanics I sem 1993-94 BITS Pialni
Operator theory, angular momentum; Schrodingers equation; time evolution; the particle in a box; simple harmonic oscillator; the hydrogen atom; molecular orbital theory; the Universal Quantum Computer; interpretations of quantum mechanics; philosophical significance;
Elementary Topology II sem 1993-94 BITS Pialni
Metric spaces; topological spaces; homeomorphisms; compact spaces; complete metric spaces; connected spaces;convergance; fixed point theorems.
Fractal Geometry I sem 1994-95 BITS Pialni
The Hausdorff measure and distance; fractal dimensions; fractal densities; projections of fractals; iterative function schemes; fractal imagecompression; fractal basin boundaries; the Mandelbrot and Julia sets.
Critical Phenomena And Phase Transitions I sem 1994-95 BITS Pialni
Phase transitions; classification; basic statistical mechanics; critical exponents; universality; scaling; microscopic models; (Landau theory; the Renormalization Group theory);self organized criticality; cellular automata.
Phase transitions in artificial intelligence; entropy and information theory; computation at phase transitions; complexity measures; Emergent behaviour at phase transitions; the computational power of dynamical systems; epsilon machine reconstruction;
Combinatorial Math II sem 1994-95 BITS Pilani
Advanced theory of permutations and combinations; elementary counting functions; theory of partitions; theorems on choice; Ramsey's theory including generalizaitons; latin squares and block designs; the mobius function; permutation groups; Polya's theorem; vector spaces; theory of generating functions; graphical enumeration problems.
Discrete Mathematical Structures I sem 1994-95 BITS Pilani
Induction, graphs, block designs, coding theory, sequences, groups, fields, Boolean algebras, analysis of algorithms etc. "a ... ground for the interaction between mathematics and modern areas of computer science".
Computability And Logic 1993-94 BITS Pilani
Models of computation; Turing machines; Abacus machines; Partial Recursive functions; Lambda calculus; LISP; Godels theorem; formal logic; the undecidability of First Order Logic; Higer order logics.
Data Structures, Algorithm Analysis and Compiler Construction 1995-96 BITS Pilani
Lists; stacks; queues; trees; tries; the theory of hashing; symbol tables; sorting; searching; graph algorithms; randomized algorithms; Data abstraction; reusability; Object Oriented Analysis and Design. Implementations in C++.
Formal specification of languages; basic automata theory; lexical analysis; regular expressions and generators; parsing; syntax directed translation; intermediate code generation. GCC, BISON, and FLEX source code. Object Oriented Compiler design
Networks And Distributed Computing 1995-96 BITS Pilani
Basic communications concepts; modems; ethernet LAN technology; network protocols: the TCP/IP suite; the BSD socket interface (through java and perl); RPCs; message passing models of distributed systems; Distributed algorithms; fault tolerance; distributed software design; concurrent object oriented programming.

Touched: Sun Jan 26 1997

The Synthesis Of Carvone	I sem 1993-94 BITS Pialni
TIC projects are campus based R&D projects done in collaboration with professionals from various industries. This particular project was aimed at developing a process route for the synthesis of an organic chemical (Carvone) which would later be scaled up for industrial production.
Chaos And Turbulence	I sem 1993-94 BITS Pialni
Turbulence was approached as one of the unsolved problems of theoretical physics. The current theories were reviewed as were similarities and differences with dynamical systems in routes to chaos and turbulence. In particular, the theories of Landau and Kolmogorov were reviewed. This project was done under the guidance of the Chemical Engineering Faculty. With the view of assisting computer simulations an interpreted language for mathematical computation and primitive graphics was developed and implemented on the Linux operating system for i386 processors.
Chaotic Dynamical Systems	II sem 1993-94 BITS Pialni
The mathematical theory of discrete dynamical systems, as developed by Devaney, was studied. The aim of this project was to develop the background and rigour required for further studies. Specific topics included: One dimensional iterative maps; the Logistic equation; critical points; hyperbolicity; Cantor sets; topological transitivity; definitions of chaos; symbolic dynamics; structural stability; Sarkovskii's theorem; Bifurcation theory; As a brief excursion, Self Organized Criticality was also studied as a related (but distinct) phenomenon. Cellular Automaton models of sandpiles were attempted.
Quantum Mechanics	I sem 1993-94 BITS Pialni
Operator theory, angular momentum; Schrodingers equation; time evolution; the particle in a box; simple harmonic oscillator; the hydrogen atom; molecular orbital theory; the Universal Quantum Computer; interpretations of quantum mechanics; philosophical significance;
Elementary Topology	II sem 1993-94 BITS Pialni
Metric spaces; topological spaces; homeomorphisms; compact spaces; complete metric spaces; connected spaces;convergance; fixed point theorems.
Fractal Geometry	I sem 1994-95 BITS Pialni
The Hausdorff measure and distance; fractal dimensions; fractal densities; projections of fractals; iterative function schemes; fractal imagecompression; fractal basin boundaries; the Mandelbrot and Julia sets.
Critical Phenomena And Phase Transitions	I sem 1994-95 BITS Pialni
Phase transitions; classification; basic statistical mechanics; critical exponents; universality; scaling; microscopic models; (Landau theory; the Renormalization Group theory);self organized criticality; cellular automata. Phase transitions in artificial intelligence; entropy and information theory; computation at phase transitions; complexity measures; Emergent behaviour at phase transitions; the computational power of dynamical systems; epsilon machine reconstruction;
Combinatorial Math	II sem 1994-95 BITS Pilani
Advanced theory of permutations and combinations; elementary counting functions; theory of partitions; theorems on choice; Ramsey's theory including generalizaitons; latin squares and block designs; the mobius function; permutation groups; Polya's theorem; vector spaces; theory of generating functions; graphical enumeration problems.
Discrete Mathematical Structures	I sem 1994-95 BITS Pilani
Induction, graphs, block designs, coding theory, sequences, groups, fields, Boolean algebras, analysis of algorithms etc. "a ... ground for the interaction between mathematics and modern areas of computer science".
Computability And Logic	1993-94 BITS Pilani
Models of computation; Turing machines; Abacus machines; Partial Recursive functions; Lambda calculus; LISP; Godels theorem; formal logic; the undecidability of First Order Logic; Higer order logics.
Data Structures, Algorithm Analysis and Compiler Construction	1995-96 BITS Pilani
Lists; stacks; queues; trees; tries; the theory of hashing; symbol tables; sorting; searching; graph algorithms; randomized algorithms; Data abstraction; reusability; Object Oriented Analysis and Design. Implementations in C++. Formal specification of languages; basic automata theory; lexical analysis; regular expressions and generators; parsing; syntax directed translation; intermediate code generation. GCC, BISON, and FLEX source code. Object Oriented Compiler design
Networks And Distributed Computing	1995-96 BITS Pilani
Basic communications concepts; modems; ethernet LAN technology; network protocols: the TCP/IP suite; the BSD socket interface (through java and perl); RPCs; message passing models of distributed systems; Distributed algorithms; fault tolerance; distributed software design; concurrent object oriented programming.