Students who entered Johns Hopkins in the current academic year should refer to the current Academic Catalog for a current list of major requirements. Students who entered Johns Hopkins University in a previous academic year should refer to the catalog of that academic year.

## Major Requirements

The listed requirements for the BA degree in mathematics are in addition to the university’s general requirements for departmental majors. Courses used to meet requirements must be completed with a grade of C- or better.

**Calculus: **Calculus I, II, and III

Majors are encouraged but not required to take honors variants.

Students usually begin by taking Calculus I-II (110.106-107), which is offered in three versions to meet the needs of students with different goals and interests.

Students in mathematics, the physical sciences, and engineering are encouraged to begin with the 110.108-109 sequence or 110.113; students majoring in other subjects may wish to take the 110.106-107 sequence, which relates the methods of calculus to the biological and social sciences.

A one-term pre-calculus course 110.105 is offered for students who could benefit from additional preparation in the basic tools (algebra and trigonometry) used in calculus. Entering students may receive course credit for Calculus I or Calculus I-II on the basis of the College Board AP exams. Students without AP credit should take the math placement exam to determine which course would be appropriate for them.

**Linear Algebra:** 110.201 Linear Algebra OR 110.212 Honors Linear Algebra

Linear Algebra (110.201), Calculus III (110.202), and Differential Equations (110.302) may be taken in any order after completing Calculus II (110.107 or 110.109). These courses are especially designed to acquaint students with mathematical methods relevant to engineering and the physical, biological, and social sciences.

The department offers honors course Honors Multivariable Calculus (110.211) and Honors Linear Algebra (110.212). Additional courses oriented toward applications include Methods of Complex Analysis (110.311), Partial Differential Equations for Applications (110.417), and Fourier Analysis and Generalized Functions (110.443).

### Analysis

110.405 Real Analysis I OR 110.415 Honors Analysis I AND one of

- 110.311 Complex Analysis
- 110.406 Analysis II
- 110.407 Honors Complex Analysis
- 110.413 Introduction to Topology
- 110.416 Honors Analysis II
- 110.417 Partial Differential Equations
- 110.421 Dynamical Systems
- 110.427 Introduction to the Calculus of Variations
- 110.439 Introduction to Differential Geometry
- 110.441 Calculus on Manifolds
- 110.443 Fourier Analysis

### Algebra

110.401 Advanced Algebra I OR 110.411 Honors Algebra I AND one of

- 110.304 Introduction to Number Theory
- 110.412 Honors Algebra II
- 110.413 Introduction to Topology
- 110.422 Representation Theory
- 110.423 Lie Groups for Undergraduates
- 110.435 Introduction to Algebraic Geometry

(Note: Students may take both 110.401 and 110.411 for credit, but only one will be used for the major requirements.)

*All students must take a basic introductory course in the foundations of abstract algebra with either 110.401 Introduction to Abstract Algebra or 110.411 Honors Algebra I, and analysis with either 110.405 Real Analysis I or 110.415 Honors Analysis I. Students interested in the theoretical foundations of mathematics may select the honors track with 110.411-2 Honors Algebra I & II and 110.415-6 Honors Analysis I & II, along with course like 110.413 Introduction to Topology and 110.439 Introduction to Differential Geometry.

Students planning to pursue further study in mathematics should work toward taking these theoretical courses as early as possible in their undergraduate years and are encouraged to take graduate-level courses as soon as they are qualified

### Elective

One more course at the 300-level or above.

### Outside course requirement

Two terms in any one of the following areas of applications of mathematics. (Note: Other appropriate, advanced, quantitative-based courses may be chosen from these or other department with the approval of the director of undergraduate studies in mathematics.)

**Physics:**171.204 Classical Mechanics, 171.301 Introduction to Electromagnetic Theory, 171.302 Topics in Advanced Electromagnetic Theory, 171.303-4 Introduction to Quantum Mechanics, 171.312 Statistical Physics and Thermodynamics, 171.405 Condensed Matter Physics**Chemistry:**030.345 Chemical Applications of Group Theory, 030.453 Intermediate Quantum Chemistry, 030.302 Physical Chemistry II**Applied Mathematics & Statistics:**550.391 Dynamical Systems, 550.420 Introduction to Probability, 550.426 Introduction to Stochastic Processes, 550.430 Introduction to Statistics, 550.453 Mathematical Game Theory, 550.471 Combinatorial Analysis, 550.472 Graph Theory**Economics:**180.301 Microeconomic Theory, 180.302 Macroeconomic Theory OR 180.402 Advanced Microeconomic Theory, 180.334 Econometrics OR 180.434 Advanced Econometrics**Philosophy:**150.420 Mathematical Logic I, 150.421 Mathematical Logic II, 150.422 Axiomatic Set Theory**Computer Science:**601.271 Automata and Computational Theory, 601.464 Artificial Intelligence, 601.442 Modern Cryptography, 601.433 Introduction to Algorithms, 600.438 Computational Genomics, 601.488 Foundations of Computational Biology, 601.461 Computer Vision, 601.457 Computer Graphics, 601.475-6 Machine Learning

## Department Honors

Department Honors are awarded to all recipients of the Bachelor of Arts degree who have also completed the following 6 courses at the combined minimum GPA of 3.6.

- 110.415-416 Honors Analysis
- 110.411-412 Honors Algebra
- 110.407 Honors Complex Analysis OR 110.607 Complex Analysis
- One more 400-level or above course

Advice:

- Honors Analysis and Honors Algebra do not depend on each other and can be taken in any order, or at the same time. However, if your plan is to take one honors course at a time, we suggest taking these courses in the order listed above.
- Students considering graduate school in mathematics are strongly encouraged to take a course from the Topology/Geometry category.