Where possible, links are provided to the Columbia University Directory of Classes.
Cognate courses are relevant graduate-level courses offered by other departments or programs. They may be selected by the student, in consultation with the student advisor, to supplement the student’s education according to his or her research interests.
For an overview of course requirements or schedule information through spring 2009, see Course Requirements & Schedule.
Also see the sample courses of study for the different Areas of Concentration.
Cognate courses are relevant graduate-level courses offered by other departments or programs. They may be selected by the student, in consultation with the student advisor, to supplement the student’s education according to his or her research interests.
For an overview of course requirements or schedule information through spring 2009, see Course Requirements & Schedule.
Also see the sample courses of study for the different Areas of Concentration.
Required Courses
- Survey of Neuroscience (G4340)
- Experimental Approaches in the Neural Sciences (G4900)
- Research in Neurobiology (G9040)
- Responsible Conduct of Neuroscience Research/Policy (G6001)
- Student Journal Club (G4990)
- Professional Skills for Neuroscientists (G4800)
Lectures, labs and student presentations will cover neuroscience from cellular and molecular biology of neurons, to human neuroanatomy and brain imaging and translational neuroscience. The first half of the semester will include a modified version of the medical school course in neuroscience and neuroanatomy. This portion of the course will include lectures and labs. In addition, a weekly journal club will include readings to expand on a topic covered during that week of the course. The second half of the semester will follow a graduate seminar course format dealing with specific topics in the properties of neurons (excitability, synaptic transmission and plasticity), sensory coding, motor control and higher brain functions. Discussion led by faculty and student presentations will expose students to the experimental approaches used to tackle problems in neuroscience and the critical skills needed to examine the broad areas covered in neuroscience research.
The goal of this course is twofold: to introduce newly entering students to research opportunities in the program and to provide training in formulating and writing a research proposal. For the first 6 weeks, faculty members from the Doctoral Program present brief talks describing their research activities. For the remainder of the semester, students participate in a grant-writing workshop. Each student writes a fellowship application that is critiqued at various stages of development by the rotation advisor, by workshop mentors and classmates. At the end of the semester, each student describes the project to the class in a brief oral presentation.
Everyone must register for this course every semester. Lab rotations are chosen according to the interests of the students. Points for this course are calculated as 15 minus any points for other courses (i.e.: if you take one course worth three points, your point count for this course will be 12 points).
Presents a set of guidelines and principles designed to allow one to deal effectively with the moral and ethical issues that are peculiar to research in science.
Student-run journal club, meeting bi-weekly Fridays at noon, for second and third year students. Students must present at least once per year. First year students are welcome to attend.
Designed to address the need for exposing advanced graduate students to the skills they need to master in preparation for successful completion of the doctorate degree, for post-doctoral training, and for eventual positions in academia or alternate careers in other science-related professions.
Advanced Neuroscience and Cognate* Courses Listed by Areas of Concentration
(Two advanced courses and one cognate course are required)Neural Development
- Advanced Eukaryotic Molecular Genetics (G4050)*
- Principles of Developmental Biology - Genetics (G4027)*
- Stem Cells and Cell Lineage Specification (G6100)*
- Introduction to Neural Development (G9002)
- Statistics for Basic Sciences (G8012)
Advanced treatment of the principles and methods of the molecular biology of eukaryotes, emphasizing the organization, expression, and evolution of eukaryotic genes. Topics include reassociation and hybridization kinetics, gene numbers, genomic organization at the DNA level, mechanisms of recombination, transposable elements, DNA rearrangements, gene amplification, oncogenes, recombinant DNA techniques, transcription and RNA splicing. Students participate in discussions of problems sets on the current literature.
The course is divided into two halves. In the first half studies in invertebrates (flies and nematodes) are used to describe the general principles that have emerged in developmental biology. The second half examines the operation of these principles in the development of various vertebrate organs and structures. Each class is in two parts. In the first part the teacher describes the subject matter, and in the second part student presentations are followed by general discussion.
The lecture series will comprise general lectures, analyses and discussions of primary literature on stem cell and lineage biology as well as student seminars. The themes to be presented include basic cell and molecular biological characterization of stem cells, regulation of self-replication versus lineage restriction and differentiation of cells, model systems used in studies of stem cells, and the relevance of tissue formation, regeneration and disease states.
Seminar on the development of vertebrate and invertebrate nervous systems with emphasis on experimental approaches. Lectures and student presentations. Mason, McCabe and Grueber.
Cellular and Molecular Neuroscience
- Biochemistry, Cell and Moleclular I (G6300)*
- Molecular Mechanisms in Synaptic Transmission (G4007)
- Biochemistry, Cell and Molecular Biology II (G6301)*
- Molecular Biophysics (G4250)*
- Molecular Pharmacology: from Membrane to Nucleus (G9600)*
- Circuits in the Brain (various topics) (G4011)
- Structure and Function of Ion Channels (G4600)
- Cellular Membranes and Organelles (G4350)*
- Advanced Seminar in Molecular and Cellular Neurobiology (G4008)
This course is for all first year Ph.D. students and provides them with a unified curriculum that covers many of the topics that students need to know to successfully carry out research in biological sciences. The topics include basic biochemical principles, processes common to all eukaryotic cells such as transcription, translation and the cell cycle, and mechanisims of cell-cell signaling.
A seminar on the cellular and molecular processes influencing synaptic transmission which will address the issue of how organelles and proteins localize to synapses by considering the transport and sorting of materials; the synthesis of proteins at synapses and mechanisms of retaining materials at synapses; the molecular mechanisms of exocytosis and endocytosis at the synapse; the physiology of synaptic transmission at excitatory and inhibitory synapses and how derangements of synaptic transmission give rise to neurological and psychiatric disorders. D.Goldberg, Bailey, MacDermott, and McCabe.
Provides a unified curriculum covering information essential to successfully carry out research in biological sciences. Topics covered in the spring term include: chromatin/telomeres, transcription, RNA processing, apoptosis, imprinting, X-inactivation, receptors, structure of signaling proteins, retroviruses/HIV, transcription factor signaling, cancer genetics and oncogenes.
Primarily intended to satisfy the requirements of graduate students. Methods and principles involved in studying the structure and function of proteins, nucleic acids, membranes and their macromolecular assemblies. Noncovalent forces and conformational analysis; ultracentrifugation, viscometry, circular dichroism, fluorescence, magnetic resonance, conformational changes in proteins and nucleic acids, topological properties of macromolecules.
The purpose of this course is to provide students with an introduction to molecular approaches to target identification and drug development and delivery for cellular and subcellular processes that contribute to human disease. Material covered includes the principles of drug-receptor interactions; ion channels as molecular targets of neurohormones and drugs; structure and function of G-protein coupled receptors; cytoplasmic signaling molecules including receptor and non-receptor tyrosine kinases and serine-threonine kinases; neuro-psychopharmacology; the pharmacology of inflammation; and novel approaches to gene-targeted pharmacology. Integration of molecular processes and human disease including cancer, neuro degenerative disease; cardiovascular disease, and psychiatric disorders is stressed.. This course is a requirement for students in the Pharmacology graduate program, but is open to all interested students. Prerequisite: familiarity with basic biochemistry and molecular biology. R.S. Kass
Modeling Biological Neurons, The Hudgkin-Huxley Neuron, Modeling and Analysis of Ion Channels, Integrate-and-Fire and other Spiking Neuron Models, Stimulus Representation and the Neural Code, Time Encoding and Stimulus Recovery, Information Representation with Time Encoding Machines, Fast Algorithms for Stimulus Recovery, Elements of Spike Processing and Neural Computation, Modeling Synapses and Synaptic Transmission, Synaptic Plasticity and Learning Algorithms.
Seminar course on the biophysical properties and the structure-function relationships of ion channels in neuronal and muscle membranes. Emphasis on biophysical, molecular, and structural approaches. Lectures and student presentations of original papers in the field. Siegelbaum, Yang and Koester.
(Interdepartmental course offered through the Integrated Program in Cellular, Molecular, and Biophysical Studies.) Introduction of eukaryotic cell biology; discussion of modern research approaches and current literature. Format: 3 hours of lecture and 1 hour of student presentation per week.
Neurobiology of Behavior and Cognition
- Imaging of Brain and Cognition (G4320)
- Behavioral Neuroscience: Views of Transformative & Translational Research (G9410)
- Statistical Analysis and Modeling of Neural Spike Data (G8285)
- Statistical Methods in Functional MRI (G8325)*
- Applied Statistics for Researchers (G6191)*
- Systems Neuroscience (G6020)
- Sound and Hearing (E4750)
- MRI for Neurosciences
- Topics in Neurobiology and Behavior (G4440)
This course focuses on the development of creative approaches to the study of human brain functions using fMRI. Lecture topics provide a working knowledge of image acquisition techniques and data analysis strategies, and the reading list will be aimed at a comprehensive selection of recent developments in neuroscience based on fMRI studies. Students select a research question and design an fMRI experiment which will be presented for class discussion and a short paper. Students will also have an opportunity to participate in on-going fMRI studies. Hirsch.
Advanced seminar on the fundamentals of brain organization, development and function in the generation and contol of behavior. Using lecture, text and original literature, a basic graduate education on neurons, circuits, systems and behavior taught by faculty experts.
We will discuss a variety of statistical methods for analyzing and modeling spike train data from single and multiple neurons. Statistical topics to be covered include: point processes; generalized linear models; regularization; state space models; Kalman and particle filtering; the Expectation-Maximization algorithm; and optimization/convexity techniques. The course will be structured around applications to neural data, including: spike-triggered averaging; estimation of neural encoding models that include spike-history and multineuronal interaction effects; estimating integrate-and-fire models from extracellular and intracellular data; performing optimal smoothing of noisy voltage- and calcium-imaging data; decoding spike trains; and estimating mutual information between stimuli and neural responses.
We will discuss a variety of statistical methods for analyzing and modeling spike train data from single and multiple neurons. Statistical topics to be covered include: point processes; generalized linear models; regularization; state space models; Kalman and particle filtering; the Expectation-Maximization algorithm; and optimization/convexity techniques. The course will be structured around applications to neural data, including: spike-triggered averaging; estimation of neural encoding models that include spike-history and multineuronal interaction effects; estimating integrate-and-fire models from extracellular and intracellular data; performing optimal smoothing of noisy voltage- and calcium-imaging data; decoding spike trains; and estimating mutual information between stimuli and neural responses.
Interests allow comparison of samples, correlation analysis, and regression analysis will be covered for continuous, categorical, censored, and multivariate data. Topics such as missing data, confounding and causation, random effects and hierarchical models, permutation tests and randomization, and non-parametric tests will be touched on. Mathematics will be eschewed and examples will abound.
This course will focus on current research topics in the neural basis of perception, cognition and sensorimotor integration, using the macaque monkey visual system as the primary experimental model. Topics covered include visual and oculomotor systems, attention, learning and plasticity, decision-making and executive function. Some didactic material will be presented by the instructors during the first two weeks of the course, but the primary format will be that of a graduate seminar. Each student will assume responsibility for one topic for one week, will extensively research the topic and will present an introductory talk 45-60 minutes in length to the rest of the class on his/her topic. All students will then read the primary papers prior to the next class session and the responsible student will lead a group discussion of the primary papers. The Instructors will provide a list of background reading and primary papers and will work with each student to prepare for their topic. Grading will be based in equal parts on: 1) the quality of background research for the project (33%), 2) quality of the class presentation (33%), and 3) participation in weekly discussions of each topic (33%). There will be no term paper or final exam.
Landmarks in the Birth of Neuroscience. Modern neuroscience incorporates topics from molecular neurobiology to cognition. It includes cell biology of neurons and glia; ion channels and electrical signaling; synaptic transmission and integration; chemical systems; brain anatomy and development; sensory systems; motor systems; higher cognitive function, and the contemplation of the puzzle of self awareness and consciousness. Academic disciplines that incorporate aspects of neuroscience include psychology, ophthalmology, biology, biochemistry, neuropharmacology, pathophysiology, neurology and psychiatry, etc. are covered within the discipline. In this course, we will review the emergence of the disciplines of neuroscience by examining landmark findings, guided by the Nobel prize awards. Each week, we will study the topic of a Neuroscience Nobel Award. We will read an original scientific paper, the Nobel prize, discuss controversies about the award selection, and contemplate how the contribution of the research is evaluated today. We will have guest lectures who have intimate knowledge of the research, in the first half of the semester. Students will present on the following topics (among other possibilties): -Review the original work for which the Nobel prize was awarded by presenting the experimental paper. -Was the award controversial at the time it was made? Read the Nobel lecture and/or a publication for which the award was given. -What were important developments that made the research possible/timely? -What is the historical consensus on the importance of the work, in retrospect (for those awards made at least a decade ago).
Animal Models of Nervous System Disorders
- Biology of Neurological and Psychiatric Disorders (G4100)
- Molecular Mechanisms of Human Disease (G6003)*
- Applied Statistics for Researchers (G6191)*
- Molecular Pharmacology: from Membrane to Nucleus (G9600x)*
Advanced seminar course on basic science approaches to schizophrenia, Alzheimer
This course will provide an in-depth analysis of several organ systems and a disease associated with each organ system. The course will have four modules; each module will describe the basic physiology, nutritional status, health and anatomy of the organ system, the genetics, cell and biochemical mechanisms and pathologies associated with the disease, as well as basic pharmacology and therapeutics to treat the disease. Enrollment is limited.
Interests allow comparison of samples, correlation analysis, and regression analysis will be covered for continuous, categorical, censored, and multivariate data. Topics such as missing data, confounding and causation, random effects and hierarchical models, permutation tests and randomization, and non-parametric tests will be touched on. Mathematics will be eschewed and examples will abound.
The purpose of this course is to provide students with an introduction to molecular approaches to target identification and drug development and delivery for cellular and subcellular processes that contribute to human disease. Material covered includes the principles of drug-receptor interactions; ion channels as molecular targets of neurohormones and drugs; structure and function of G-protein coupled receptors; cytoplasmic signaling molecules including receptor and non-receptor tyrosine kinases and serine-threonine kinases; neuro-psychopharmacology; the pharmacology of inflammation; and novel approaches to gene-targeted pharmacology. Integration of molecular processes and human disease including cancer, neuro degenerative disease; cardiovascular disease, and psychiatric disorders is stressed.. This course is a requirement for students in the Pharmacology graduate program, but is open to all interested students. Prerequisite: familiarity with basic biochemistry and molecular biology. R.S. Kass
Theoretical Neuroscience
- Computational Neural Modeling and Neuroengineering (E6480)
- Theoretical Neuroscience (G4360)
- Advanced Topics in Theoretical Neuroscience (G6040)
- Comp. Neuro.: Circuits in the Brain (W4020)
Engineering perspective on the study of multiple levels of brain organization, from single neurons to cortical modules and systems. Mathematical models of spiking neurons, neural dynamics, neural coding, and biologically-based computational learning. Architectures and learning principles underlying both artificial and biological neural networks. Computational models of cortical processing, with an emphasis on the visual system. Applications of principles in neuroengineering; neural prostheses, neuromorphic systems and biomimetics. Course will include a computer simulation laboratory.
This course will provide a comprehensive introduction to the field of computational neuroscience, covering three broad areas: mathematical techniques, computer simulation methods, and modeling neural systems. Mathematical techniques will include solution of ordinary differential equations, matrix diagonalization including eigenvalues and eigenvectors, principal components analysis, and information theory. Computer simulations will be done using Matlab and will involve methods of numerical integration of nonlinear differential equations, minimization and stochastic approaches, among other numerical methods. Course exercises will include construction of models of channels, single neurons, synapses, small circuits of neurons and large networks, and explorations of neural coding, selectivity, memory, and supervised, unsupervised and reward-based forms of learning. Abbott.
Lectures combined with reading and discussion of relevant papers. Topics and instructors will vary from year to year with the interests both of the instructors and the students, but possible topics include: Models of decision-making at the cognitive and neural level; Models of pattern-formation in neural development; Models of memory; Models of cortical circuitry; Reinforcement learning; Mean-field, Fokker-Planck, and replica methods in analyzing neural circuits; Redundancy, synergy and spike timing in neural coding; Information-theoretic and maximum-entropy methods in neural coding and neural data analysis; Bayesian models of sensory and motor function; Optimization approaches to understanding the nervous system; etc. Miller.
The Biophysics of Computation: Modeling Biological Neurons, The Hudgkin-Huxley Neuron, Modeling Channel Conductances and Synapses as Memristive Systems, Bursting Neurons and Central Pattern Generators, I/O Equivalence and Spiking Neuron Models. Information Representation and Neural Encoding: Stimulus Representation with Time Encoding Machines, The Geometry of Time Encoding, Encoding with Neural Circuits with Feedback, Population Time Encoding Machines. Dendritic Computation: Elements of Spike Processing and Neural Computation, Synaptic Plasticity and Learning Algorithms, Unsupervised Learning and Spike Time-Dependent Plasticity, Basic Dendritic Integration. Projects in Matlab or Python.
Some Cognate Courses for Theoretical Neuroscience*
- APMA: Asymptotic Methods In Applied Mathematics(E8308y)*
- APMA: Applied Mathematics III: Dynamical Systems (E4101x)*
- APMA: Introduction to Biophysical Modeling (E4400)*
- EE: Signals and Systems (E3801)*
- EE: Information Theory (E6717x)*
- Physics: Mathematical Methods in Physics (G4019)*
- Physics: Statistical Mechanics (G6036)*
- Physics: Scientific Computing (G6080)*
- Computer Science: Scientific Computation (W3210)*
- Computer Science: Machine Learning (W4771)*
- Cellular: Molecular Genetics (G4150*)
Asymptotic treatment of ordinary and partial differential equations in problems arising in applied mathematics. Asymptotic series. Asymptotic evaluation of integrals. Expansion of solutions of ordinary differential equations: connection problem and turning points. Stoke
An introduction to the analytic andNeuroscience* geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Theorem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov-Hopf; sensitive dependence and chaotic dynamics; selected applications.
Introduction to physical and mathematical models of cellular and molecular biology. Physics at the cellular scale (viscosity, heat, diffusion, statistical mechanics). RNA transcription and regulation of genetic expression. Genetic and biochemical networks. Bioinformatics as applied to reverse-engineering of naturally-occurring networks and to forward-engineering of synthetic biological networks. Mathematical and physical aspects of functional genomics.
Modeling, description, and classification of signals and systems. Continuous and discrete-time systems. Time domain analysis, differential equations, and convolution. Fourier series. Fourier and Laplace transforms. Frequency domain analysis, transfer functions. Amplitude and frequency modulation. Frequency response and Bode plots. Filtering. Stability and root locus. Use of modern mathematics and simulation software packages for signal and system analysis, such as MATLAB.
The source coding theorem. The capacity of discrete memoryless channels and the noisy channel coding theorem. The rate distortion function. Discrete memoryless sources and single-letter distortion measures. Bhattacharya bounds, convolutional codes, and the Viterbi algorithm.
Highlights of complex analysis, differential equations, integral equations, Green
Fundamentals of statistical mechanics; theory of ensembles; quantum statistics; imperfect gases; cooperative phenomena.
Computational techniques for scientific problems with emphasis on practical applications and effective programming. Review of computers, programming, floating-point numbers, and numerical stability. Survey of basic numerical algorithms and numerical subroutine libraries and their application to scientific problems.
Introduction to computation on digital computers. Design and analysis of numerical algorithms. Numerical solution of equations, integration, recurrences, chaos, differential equations. Introduction to Monte Carlo methods. Properties of floating point arithmetic. Applications to weather prediction, computational finance, computational science, and computational engineering.
Topics from generative and discriminative machine learning including least squares methods, support vector machines, kernel methods, neural networks, Gaussian distributions, linear classification, linear regression, maximum likelihood, exponential family distributions, Bayesian networks, Bayesian inference, mixture models, the EM algorithm, graphical models and hidden Markov models. Algorithms implemented in Matlab.
Cellular Molecular Biophysics
* denotes cognate course
