ACADEMIC COURSES FOR 2016Course

Programme Home page


The following two Courses will be offered by NIAS Consciousness Studies Programme during the second half of 2016. If you wish to enroll for any of the Courses below write to niasconsciousnessprogramme@gmail.com Please read the Course details to know about Course requisites. Last date to send your email with interest is 8 August 2016.

Course CSP-3-1: Scientific Theories of Consciousness – I: Mathematical Methods Course Instructor and Concept: Nithin Nagaraj
Course CSP-2-2: Conceptual Mathematics Course Instructor and Concept: Venkat Rayudu


Course CSP-3-1: Scientific Theories of Consciousness – I: Mathematical Methods (3 credits)
Course Instructor and Concept: Nithin Nagaraj
Credit Hours: Three hours/week (2 hours lecture + 1 hour lab session)
Course Duration: August-November 2016, Monday 10:30 -12:30 pm, Thursday 3:30 - 4:30 pm

To enrol write to niasconsciousnessprogramme@gmail.com before 8 August 2015

Course Description: “Scientific Theories of Consciousness-I” is the first course of a two-part series. In “Part-I: Mathematical Methods”, we shall uncover the mathematical foundations that form the bedrock of several scientific theories of consciousness. Understanding ‘consciousness’ remains the final frontier of research and is increasingly becoming an interdisciplinary field of study with ideas and principles borrowed from several mathematical disciplines such as Information Theory, Signal Processing, Time Series Analysis, Chaos Theory, Complexity Measures, Brain Imaging Analysis, Network & Graph Theory. This course will equip the student with mathematical methods required to undertake basic research in scientific theories of consciousness.

Learning Objectives: The primary objective of this course is to equip the student with the required mathematical methods, principles and techniques in order to undertake research in scientific theories of consciousness which is the subject matter of Part-II of this course to be offered in the next semester. The mathematical skills needed to build, analyze and rigorously evaluate a scientific theory of consciousness will be the key learning of this course.

Pre-requisites for registration/auditing: Familiarity with elementary set theory and calculus with an interest in mathematics is a must. It is highly recommended that the student be comfortable with any one computer programming language of her choice (MATLAB/Python/C/any-other-equivalent-computer-language). This course will be intensive in mathematical reasoning and programming. Students will solve assignments that involve mathematical and logical thinking (including writing mathematical proofs), as well as writing computer programs as an aid to understanding the mathematical principles.

Expected Student Workload: There will be a 2-hour lecture session and 1-hour lab session every week. The lecture session will introduce the various mathematical principles. The lab session will involve problem solving, writing mathematical proofs as well as writing computer programs. Assignments (both graded and ungraded, reading and writing) will be given extensively throughout the course.

Lecture Topics and Discussion
Module 1 Introduction to scientific theories of consciousness, methods of science, the role of mathematics in scientific theories with emphasis on its role in cognitive science, neuroscience, and existing scientific theories of consciousness; the unreasonable effectiveness of mathematics, and limits of mathematical reasoning; a bird’s eye-view of the various mathematical methods needed for understanding scientific theories of consciousness.

Module 2 Basics of linear algebra: “y=Ax”, the four fundamental spaces of linear algebra, vector spaces and linear transformations, foundations of singular value decomposition and principal component analysis; probability theory basics, introduction to random variables and stochastic processes, Markov processes, linear and nonlinear processes.

Module 3 Time series analysis basics, linear and nonlinear signal processing fundamentals, introduction to the four Fourier representations and its properties, basics of Wavelet transforms, signal processing algorithms used in neuroscience; introduction to non-linear dynamics/chaos theory and its applications in brain imaging analysis. Introduction to advanced techniques such as compressed sensing, signal processing on graphs, and dynamics on networks; basics of biostatistics, hypothesis testing, interpretation of statistical tests, and the role of statistics in scientific theories of consciousness.

Module 4 Introduction to Information Theory and complexity measures, Shannon’s coding theorems, role of information theory in the biological sciences (with emphasis to neuroscience and cognitive science), different notions of information (extrinsic, intrinsic, semantic, double-aspect information and quantum information); introduction to various measures of consciousness (such as causal density, neural complexity, differentiation-integration measures of brain complexity and dynamics, perturbational complexity index and others); introduction to Tononi’s Integrated Information Theory of Consciousness. Note: These theories will be exhaustively and rigorously dealt in Part-II of the course (to be offered in the next semester).

Basis for Final Grades Class Participation: 5% Take-home Assignments: 10% (reading+writing, weekly) Quiz: 20% (2 quizzes) Lab assignments: 15% Mid-term Exam: 20% Final Exam: 30%

 

Course CSP-2-2: Conceptual Mathematics (2 credits)
Course Instructor and Concept: Venkat Rayudu
Course Duration: August-November 2016

To enrol write to niasconsciousnessprogramme@gmail.com before 8 August 2015

Course Description: Conceptual Mathematics, the grammar of mathematics, provides a general account of the workings of mathematical methods.

The Conceptual Mathematics course provides a first introduction to category theory, which embodies these general principles of calculation common to arithmetic, algebra, calculus, geometry, and logic. Basic concepts of category theory are introduced in a manner comprehensible to a student body of diverse academic backgrounds. Major topics of category theory covered in the course include: sets and functions, category of dynamical systems, structure-preserving maps, universal mapping properties, and definitions of multiplication, addition, and truth.

Learning Objectives: The main objective of the Conceptual Mathematics course is to demystify mathematics and thereby make mathematical sciences more user-friendly. The present course emphasizes understanding why and how mathematical calculations give the results that they do (e.g. 1 + 2 = 3). Upon completion of the course, students will have a clear understanding of the basics of extracting the mathematical content of a given subject matter. This course will prepare students for advanced category theoretic studies of mind, consciousness, and cognition - the “Science of Knowing” course offered next semester.

Pre-requisites for registration/auditing: The course is based on Lawvere and Schanuel’s Conceptual Mathematics textbook, which is addressed to total beginners. The concepts and constructions of category theory are introduced informally in terms of examples drawn from everyday experience. No mathematical training beyond that of high school mathematics is required for registering / auditing the course.

Expected Student Workload: The course syllabus will be covered in 16 weeks, with one 2-hour lecture per week. Successful completion of the course involves: (i) class participation, (ii) take-home assignments, (iii) class presentation, (iv) in-class exams, and (v) term paper. There will be two in-class exams (mid-term and final), two take-home assignments of exercises from the Conceptual Mathematics textbook, and one class presentation of an exercise selected by the student. The topic of the term paper is also selected by the student and in consultation with the instructor.

Lecture Topics and Discussion:

The following course lectures are based on the corresponding material in Lawvere and Schanuel’s Conceptual Mathematics textbook.

1. Sets and Functions
2. Composition of Functions
3. Types of Functions
4. Functions vs. Figures
5. Definition of Category
6. Structure-Preserving Map
7. Examples of Categories
8. Category of Dynamical Systems
9. Natural Number Object
10. Universal Mapping Property
11. Definition of Product
12. Sums
13. Actions
14. Exponentiation
15. Truth Value Object
16. Logical Operations

Basis for Final Grades:
Class Participation: 5% Take-home Assignments: 10% (2 x 5) Class Presentation: 10% Mid-term Exam: 20% Term Paper: 25% Final Exam: 30%