The information here is taken from the course catalog and supplemented with information from students.

### Computer Science

**Math Courses Recommended:** Math 152, 157

If you have no prior experience with coding, CS 1 or CS 50 are great courses to learn basic coding skills. Beyond these courses, there are a number of theoretical CS courses that tend to be more mathematical.

**Computer Science 121: Introduction to the Theory of Computation** (fall)

*Course Content:* CS 121 is a general introduction to the theory of computation, teaching how to reason precisely about computation and prove mathematical theorems about its capabilities and limitations. Topics include finite automata, Turing machines, formal languages, computability, uncomputability, computational complexity, and the P vs. NP question.

*Prerequisites*: Exposure to proofs and discrete math (CS 20).

*Expected Workload:* 7 – 10 hours/week

**Computer Science 124: Data Structures and Algorithms** (spring)

*Course Content:* CS 124 covers the design and analysis of efficient algorithms and data structures. Algorithm design methods, graph algorithms, approximation algorithms, and randomized algorithms are discussed.

*Prerequisites*: Exposure to programming (CS 50 or equivalent). Some exposure to discrete applied mathematics (Applied Math 106 or 107, CS 121 or Stat 110)

*Expected Workload:* 8 – 20 hours/week

**Note:** Computer Science 125 (fall) is an accelerated introduction to theoretical computer science for students with strong mathematical preparation, to be taken in place of both Computer Science 121 and 124.

**Further courses to consider:** CS 109, 127, 181 and 182

### Applied Math

**Applied Math 105: Ordinary and Partial Differential Equations** (fall)

*Course Content:* Applied Math 105 is an introduction to differential equations (a topic not well-covered in the math department), including power series solutions, special functions, eigenfunction expansions, elementary partial differential equations, separation of variables, and a brief introduction to nonlinear dynamical systems and numerical methods.

*Prerequisites:* Multivariable calculus and linear algebra (Math 21a/b or equivalent)

*Expected Workload:* 5 – 10 hours/week

**Applied Math 120: Applied Linear Algebra and Big Data** (spring)

*Course Content:* Applied Math 120 covers topics in linear algebra with an emphasis on applications, including principal component analysis, singular value decomposition, data mining methods, and others. Applications include analysis of data in the physical sciences, biology, climate, commerce, internet, image processing, economics and more.

*Prerequisites:* Multivariable calculus and linear algebra (Math 21a/b or equivalent), exposure to programming (CS 50 or equivalent).

*Expected Workload:* 4 – 10 hours/week

**Applied Math 121: Introduction to Optimization: Models and Methods** (fall)

*Course Content:* Applied Math 121 is an introduction to stochastic optimization, including linear programming, branch programming, branch-and-cut, Markov chains, and Markov decision processes. There is an emphasis on modeling.

*Prerequisites:* Multivariable calculus and linear algebra (Math 21a/b or equivalent), some knowledge of probability and statistics (Statistics 110 or equivalent).

*Expected Workload:* 8 – 12 hours/week

**Further courses to consider:** AM 104, 106, 111, 115

For further information about Applied Math courses at Harvard, see here and here.

### Statistics

**Math Courses Recommended:** Math 154, Math 155r

**Statistics 110: Introduction to Probability** (fall)

*Course Content:* Statistics 110 is a comprehensive introduction to probability, as a language and set of tools for understanding statistics, science, risk, and randomness. Topics include probability basics, univariate distributions, multivariate distributions, limit laws and Markov chains, transition probabilities, stationary distributions, and convergence.

*Prerequisites:* Single-variable calculus (AP Calculus BC or Math 1b)

*Expected Workload:* 7 – 14 hours/week

**Statistics 111: Introduction to Theoretical Statistics** (spring)

*Course Content:* Statistics 111 discusses basic concepts of statistical inference from frequentist and Bayesian perspectives. Topics include maximum likelihood methods, confidence and Bayesian interval estimation, hypothesis testing, least squares methods and categorical data analysis.

*Prerequisites:* Introductory probability (Statistics 110)

*Expected Workload:* 7 – 14 hours/week

**Further Courses to Consider:** Statistics 139 and 171

### Physics

**Math Courses Recommended:** One of Math 21/23/25/55, Math 115, Math 122, Math 132, and Math 136.

**Physics 15a/b/c: Introductory Mechanics and Relativity, Introductory Electromagnetism and Statistical Physics, Wave Mechanics** (both semesters)

*Course Content:* Physics 15a/b/c cover the necessary introductory material to concentrate in physics. If you’re interested in concentrating, it is strongly recommended that you take Physics 15a either your freshman fall or spring. Students with strong background frequently substitute Physics 15a with Physics 16 (see below) or Physics 151, Physics 15b with Physics 153, and Physics 15c with Physics 175.

*Prerequisites:* Knowledge of basic physics using algebra (AP Physics 1 and 2), though calculus-based physics (Physics C) is recommended. Single-variable calculus (AP Calculus BC or Math 1b) is needed, and multivariable calculus (Math 21a) is often taken simultaneously with Physics 15a.

*Expected Workload:* 4 – 10 hours/week

**Physics 16: Mechanics and Special Relativity** (fall)

*Course Content:* Physics 16 is a very intensive yet highly satisfying introduction to college-level mechanics and special relativity, covering topics like the Lagrangian, 4-vectors, the moment of inertia tensor, and Euler’s equations. The main focus of this course is on problem sets, which can be very challenging, and on the community that naturally develops every year at Physics Night. This course can be an outstanding experience but is only recommended if you have a strong math and physics background.

*Prerequisites:* Calculus-based mechanics (AP Physics C) and single-variable calculus (AP Calculucs BC or Math 1b) are required. Multivariable calculus (Math 21a) and linear algebra (Math 21b) are recommended. Background in differential equations can also be helpful.

*Expected Workload:* 7 – 15 hours/week

**Further Courses to Consider:** Physics 143ab, 181, and many others.

For further information about physics courses at Harvard, look at the booklet published by the Physics Department or speak to Professor Georgi or Dr. Morin.

### Philosophy and Logic

**Math Courses Recommended:** Math 145a (or anything in the 140s)

**Philosophy 140: Fundamentals of Logic** (fall)

*Course Content:* Philosophy 140 is an introduction to logic, covering the central concepts of logic, basic elements of modal theory, applications to mathematics, and some higher-order logic and non-constructive systems.

*Prerequisites:* None, but exposure to proofs is recommended.

*Expected Workload:* 4 – 10 hours/week

**Philosophy 145: Modal Logic** (spring)

*Course Content:* Philosophy 145 is an introduction to the semantics and metatheory of modal logic as well as some of its applications in philosophy and linguistics. Topics may include completeness, frames, and incompleteness for propositional modal logic; semantics for quantificational modal logics; provability interpretations of modal logic; intensional semantics for conditionals and other natural language expressions.

*Prerequisites:* Exposure to proofs and some familiarity with logic (Philosophy 140).

*Expected Workload:* 3 – 8 hours/week

**Further Courses to Consider:** EMR 17, Philosophy 144, Philosophy 242

### Economics and Finance

**Math Courses Recommended:** Math 18 (or higher level), 117, 157

**Economics 1011a: Intermediate Microeconomics: Advanced** (fall)

*Course Content:* Economics 1011a covers the basics of the microeconomics of consumers, firms, and markets at a mathematical level and applies them to a wide range of human behavior.

*Prerequisites:* Multivariable calculus (Math 21a or equivalent).

*Expected Workload:* 5 – 15 hours/week

**Further Courses to Consider:** Economics 1011b

### Chemistry and the Life Sciences

**Math Courses Recommended:** Math 19 (or higher level), 153, 243

**Chemistry 20/30: Organic Chemistry** (full year)

*Course Content:* Chemistry 20/30 form the organic chemistry sequence strongly recommended for students interested in learning more about the physics or chemistry of organic molecules. Chemistry 20 (spring) provides an introduction to bonding theory, mechanisms, some basic organic reactions, and spectroscopy. Chemistry 30 (fall) provides notoriously rigorous coverage of organic reactions, with a focus on carbonyl chemistry, pericyclic reactions, and stereochemistry, as well as an understanding of the mechanistic behavior of organic molecules.

*Prerequisites:* Knowledge of elementary chemistry (AP Chemistry)

*Expected Workload:* 10 – 20 hours/week

**Life Sciences 50a/b: Integrated Science** (full year)

*Course Content:* Life Sciences 50a/b is a highly intensive, two-semester double course (i.e. it meets twice as many times as a regular course) that integrates math, statistics, computer science, physics, chemistry, and biology to explore major biological problems. It provides an introduction to a wide variety of areas including multivariable calculus, linear algebra, statistical mechanics, fluid mechanics, Markov processes, graph theory, biochemistry, protein synthesis, population dynamics, and much, much more.

*Prerequisites:* Knowledge of single-variable calculus (Math 1b or AP Calculus BC), elementary physics (AP Physics), chemistry (AP Chemistry), and biology (AP Biology).

*Expected Workload:* 10 – 30 hours/week

**Further Courses to Consider:** Chemistry 17/27, 40, 60, 160, 161, 242, and Life Sciences 1a/b.

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