ACADEMIC COURSES FOR 2016 



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 CSP31: 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: AugustNovember 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 ConsciousnessI” is the first course of a twopart series. In “PartI: 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 PartII 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. Prerequisites 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/anyotherequivalentcomputerlanguage). 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 2hour lecture session and 1hour 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 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 nonlinear 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, doubleaspect information and quantum information); introduction to various measures of consciousness (such as causal density, neural complexity, differentiationintegration 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 PartII of the course (to be offered in the next semester). Basis for Final Grades Class Participation: 5% Takehome Assignments: 10% (reading+writing, weekly) Quiz: 20% (2 quizzes) Lab assignments: 15% Midterm Exam: 20% Final Exam: 30% 

Course CSP22: Conceptual Mathematics (2 credits) 

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, structurepreserving 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 userfriendly. 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. Prerequisites 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 2hour lecture per week. Successful completion of the course involves: (i) class participation, (ii) takehome assignments, (iii) class presentation, (iv) inclass exams, and (v) term paper. There will be two inclass exams (midterm and final), two takehome 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 Basis for Final Grades: 
