Courses

Calculus, Fourier transforms, probability theory, scientific programming in Python.

Multivariate calculus and linear (or, alternatively, matrix) algebra

Mathematics for engineers and physicists

Partial differential equations.
Some knowledge of Python, MATLAB or other language is preferred.

Solid undergraduate linear algebra. Confident in following and constructing proofs. Some prior knowledge of the representation theory of finite groups is helpful but not completely necessary. Discuss this carefully with your academic mentor.

Single-variable and multi-variable calculus, Linear algebra, ordinary differential equations, real analysis, or equivalent knowledge.

B36 “Introduction to Real Analysis” is recommended but not required. The following is expected prerequisite knowledge: basic set theory, mathematical logic, the fundamental property of real numbers; familiarity with limit definitions, and how to use these definitions in rigorous proofs of sequences, continuity and differentiation of real-valued functions; properties of a supremum (or least upper bound) and infimum (or greatest lower bound); basic topology including the definitions of open, closed, compact sets in the Euclidean space; basic definitions and properties of Riemann integrals. Please contact the instructor at the beginning of the course with questions.

Python and/or R programming, linear algebra, B49 Dynamical systems

Students should have a robust understanding of undergraduate-level calculus, single and multivariable. Familiarity with differential equations would also be beneficial.

Programming in Python, e.g B50 Introduction to Scientific Computing. Basic knowledge in neuroscience, e.g. B52 Introduction to Neuroscience or A310 Computational Neuroscience, and statistical machine learning, e.g B46 Introduction to Machine Learning or B1 Statistical Tests, is preferred.

Single-variable and multi-variable calculus, linear algebra, B36 Real Analysis, A110 Measure Theory, or equivalent.

A114 Functional Analysis and A108 Partial Differential Equations, or equivalent.

Required pass in first theoretical portion of this course, A111 Nonlinear Time series Analysis and Manifold Learning.
Prior deep knowledge of Taken’s theorem-based methods is an absolute prerequisite.

Quantum Mechanics

Quantum Mechanics and B11 Classical Electrodynamics

Undergraduate organic chemistry and/or biochemistry or related chemistry

B11 Classical Electrodynamics, A203 Advanced Optics

Quantum Mechanics

companion course to A203 Advanced Optics

Undergraduate chemistry

Assumes undergraduate organic chemistry or biochemistry.

Basic quantum mechanics and basic concepts of statistics.

Maxwell’s equations in differential form. Solving Maxwell’s equations to obtain electromagnetic waves. Linear algebra of vectors and matrices.

Undergraduate level biochemistry or molecular biology

Maxwell’s equations in differential form. Solving Maxwell’s equations to obtain electromagnetic waves. Quantum mechanics.

Undergraduate level of condensed matter physics

Undergraduate ordinary and partial differential equations and/or A104 Vector and Tensor Calculus, or equivalent

Classical Mechanics and Quantum Mechanics to advanced undergraduate level.

Undergraduate-level knowledge of general chemistry; Advanced-level knowledge of organic chemistry.

Undergraduate quantum mechanics (full year), especially quantum matrix mechanics for spin, Schrodinger equation (stationary and time dependent), and the operator treatment of the quantum harmonic oscillator.

Quantum Mechanics and ideally Advanced Quantum Theory. A further background in Quantum Field Theory and Statistical Physics is helpful.

Statistical Physics (B12) or Statistical Mechanics, Critical Phenomena and Renormalization Group (A225); anything equivalent to a basic course on Nonrelativistic Quantum Mechanics.

Undergrad-level quantum mechanics and linear algebra

Linear algebra, probability and statistics. Introductory knowledge of quantum information is helpful, although quantum bits, operations and measurements will be covered here.

Graduate classical/analytical mechanics
B10 Analytical Mechanics, B13 Fluid Mechanics

Cell biology and/or genetics

Cell biology and/or genetics

Neuroscience background required

Advanced undergraduate Cell Biology and Genetics

Introductory neuroscience, computational methods, programming, mathematics.

Background in neuroscience (either at the BSc/MSc level or the OIST basic neuroscience course). Cellular neurophysiology and neuroanatomy.

B46 Introduction to Machine Learning and programming experience in Python, C or C++ are required. Basic calculus of vectors and matrices and differential equations are assumed.

Students should have previously taken at least two basic courses in neuroscience or have completed the equivalent by documented prior learning

Introductory neuroscience and preparation in one or more areas of linear algebra, machine learning, or behavioral ecology is recommended.

Basic knowledge of cellular biology and neurobiology.

Passing “Introduction to Neuroscience” or equivalent is required.

Basic knowledge of cellular biology and neurobiology. Passing “Introduction to Neuroscience” or equivalent is required.

Basic understanding of evolutionary and cell biology at the undergraduate level is assumed. e.g., B27 Molecular Biology of the Cell or B23 Molecular Evolution

Molecular Biology and Genetics required, e.g.: B27 Molecular Biology of the Cell and B35 Genetics and Modern Genetic Technologies

Undergraduate biology, especially evolution. Course B23 Molecular Evolution is required. Contact Prof Sallan if you seek an exemption.

Undergraduate mathematics.

College level introductory physics or permission of instructor, mathematics for physics.

Undergraduate mechanics and a firm grasp of calculus and vector mathematics

Undergraduate calculus and algebra.

B10 Analytical Mechanics and/or A104 Vector and Tensor Calculus.

B10 Analytical Mechanics and/or A104 Vector and Tensor Calculus.

No prior knowledge assumed

Biology, chemistry, and/or physics at undergraduate levels

Assumes general knowledge in biology

This is a basic level course, that will be adjusted accordingly to the interests of enrolled students. No prior knowledge assumed.

The course is very basic. Non-biology students are welcome.

Familiarity with real and complex numbers will be assumed. Ideally, students will have had some previous exposure to mathematical proofs, though this is not strictly required.

Basic knowledge of elementary mathematics such as differentiation, integration, and elementary linear algebra. However, whenever necessary, mathematical details will be explained.
Students will need to write some code in Python

Undergraduate chemistry

Undergraduate Calculus or equivalent is required. Multivariable calculus is not a prerequisite. If you are not sure about the prerequisite material, please contact the instructor before enrolling.

A basis in cognitive science (any discipline) is preferred. Please consult with Prof Froese before enrolling.

There are no prerequisites for this course. Students will be expected to complete assigned readings ahead of class in order to participate fully.

Undergraduate-level coursework in general biology and calculus are recommended but not required.

Curiosity and sense of wonder

Fundamental undergraduate-level physics recommended but not required.

No prerequisites. However, without some mathematics and programming background, topics like deep learning are hard to follow.

Basics of calculus, linear algebra, and programming.

Classical mechanics, e.g. B10

Basic skills of computer use.
Familiarity with linear algebra and basic differential equations is assumed, but the course aims to help intuitive understanding of such mathematical concepts by computing and visualization.

undergraduate quantum mechanics and linear algebra

Undergraduate biochemistry, biology, and chemistry