Math Course Placement and Sequencing for All Homewood Students
There are three different versions of single variable calculus offered by the Mathematics Department, including 2 versions of semester courses in Calculus I and II, roughly equivalent to Calculus AB and BC in the College Board’s Advanced Placement (AP) system, and a single semester honors version encompassing both Calculus I and II. Students should select their first course in mathematics at JHU based on their intended areas of study, prior experience and training in mathematics, and the results of an advisory Mathematics Placement Process, mandatory for incoming first-year students. Students intending to major in mathematics, the natural sciences, or engineering, or who are interested in studying mathematics beyond a year of single variable calculus are strongly encouraged to begin with the AS.110.108 Calculus I (Physical Sciences & Engineering) - AS.110.109 Calculus II (For Physical Sciences and Engineering) sequence or AS.110.113 Honors Single Variable Calculus. Students majoring in other subjects, or who do not intend to continue taking mathematics courses beyond a year of calculus, may wish to take the sequence AS.110.106 Calculus I (Biology and Social Sciences) - AS.110.107 Calculus II (For Biological and Social Science). This latter sequence relates the methods of calculus to the biological and social sciences. A one-semester precalculus course (AS.110.105 Precalculus) is offered for students who would benefit from practice modeling with tools used in calculus.
Entering students may receive course credit for Calculus I or Calculus I and II on the basis of the performance level on either the AP or International Baccalaureate (IB) exams. All students, regardless of completion of advanced placement exams previously, must engage with a Mathematics Placement Process to determine their appropriate first course in mathematics. Additional placement information can be found here.
After completing a full year of calculus, the courses AS.110.201 Linear Algebra, AS.110.202 Calculus III, or AS.110.302 Differential Equations and Applications may be taken in any order. The department offers honors courses of the former 2; AS.110.212 Honors Linear Algebra and AS.110.211 Honors Multivariable Calculus.
Students entering the program with advanced training, for example, courses completed either within high school or at another university or college that are above single-variable calculus, may petition the department for a personal assessment of how well these courses compare to what we offer here at Johns Hopkins. Should the courses compare well, the department may offer either a credit transfer or course waiver from having to take the comparable course(s) here at Johns Hopkins. Contact the department's Director of Undergraduate Studies for more information.
Mathematics Major Requirements
(Also see Requirements for a Bachelor's Degree.)
The undergraduate program in the Department of Mathematics is intended both for students interested in preparing for graduate study and research in pure mathematics, and for students interested in using mathematics to pose and solve problems in the sciences, engineering, social sciences, or other areas. Undergraduate mathematics majors will study:
- The foundations of analysis, which begins with the study of functions and their derivatives and integrals
- The fundamentals of advanced algebra, which is based on axiomatic systems involving operations of addition and multiplication in general settings
- Additional subjects such as geometry, probability, and topology
- Applications of mathematics to science and/or engineering.
Writing and Communication in the Major - Students must complete at least 6 credits of Writing and Communication foundational ability coursework in one major. For this upcoming 2024-2025 academic year, candidates for the Bachelor of Arts degree in Mathematics will be able to fulfill this requirement by selecting 6 credits of electives or other courses in the major that are designated as Writing and Communications courses. The program is updating their curriculum and will include courses designated as Writing and Communications courses within the major starting in the 2025-2026 academic year.
A candidate for the Bachelor of Arts degree in Mathematics is required to have completed the major requirements listed below. All courses used to meet these requirements must be completed with a grade of C- or better and may not be taken satisfactory/unsatisfactory (S/U) grading scheme.
| Code | Title | Credits |
|---|---|---|
| AS.110.106 | Calculus I (Biology and Social Sciences) | 4 |
| or AS.110.108 | Calculus I (Physical Sciences & Engineering) | |
| AS.110.107 | Calculus II (For Biological and Social Science) 1 | 4 |
| or AS.110.113 | Honors Single Variable Calculus | |
| or AS.110.109 | Calculus II (For Physical Sciences and Engineering) | |
| AS.110.202 | Calculus III 2 | 4 |
| or AS.110.211 | Honors Multivariable Calculus | |
| AS.110.201 | Linear Algebra 2 | 4 |
| or AS.110.212 | Honors Linear Algebra | |
| AS.110.401 | Introduction to Abstract Algebra | 4 |
| or AS.110.411 | Honors Algebra I | |
| AS.110.304 | Elementary Number Theory 2,3 | 4 |
| or AS.110.412 | Honors Algebra II | |
| or AS.110.413 | Introduction To Topology | |
| or AS.110.422 | Representation Theory | |
| or AS.110.435 | Introduction to Algebraic Geometry | |
| AS.110.405 | Real Analysis I 2 | 4 |
| or AS.110.415 | Honors Analysis I | |
| AS.110.311 | Methods of Complex Analysis | 3-4 |
| or AS.110.406 | Real Analysis II | |
| or AS.110.407 | Honors Complex Analysis | |
| or AS.110.413 | Introduction To Topology | |
| or AS.110.416 | Honors Analysis II | |
| or AS.110.417 | Partial Differential Equations | |
| or AS.110.421 | Dynamical Systems | |
| or AS.110.439 | Introduction To Differential Geometry | |
| or AS.110.441 | Calculus on Manifolds | |
| or AS.110.443 | Fourier Analysis | |
| One 300-level or higher math course 4 | 4 | |
| Two courses in any one of the approved applications of mathematics or other courses approved by the Director of Undergraduate Studies. 5 | 8 | |
| Total Credits | 43-44 | |
- 1
Honors Single Variable is a single 4 credit course that will count toward the major or minor in mathematics as both Calculus I and Calculus II.
- 2
Majors are encouraged but not required to take honors variant.
- 3
AS.110.413 Introduction To Topology cannot be used for more than one requirement.
- 4
Math courses are defined as courses AS.110.xxx
- 5
See table below for some examples of approved application courses. All other choices must be approved by the Director of Undergraduate Studies, and must be upper-level, quantitative in nature, and both from the same department or program.
Approved Courses in Areas of Application
| Code | Title | Credits |
|---|---|---|
| Physics | ||
| AS.171.204 | Classical Mechanics II | 4 |
| AS.171.301 | Electromagnetic Theory II | 4 |
| AS.171.303 | Quantum Mechanics I | 4 |
| AS.171.304 | Quantum Mechanics II | 4 |
| AS.171.312 | Statistical Physics/Thermodynamics | 4 |
| Chemistry | ||
| AS.030.302 | Physical Chemistry II | 3 |
| AS.030.453 | Intermediate Quantum Chemistry | 3 |
| Economics | ||
| AS.180.301 | Microeconomic Theory | 4 |
| AS.180.302 | Macroeconomic Theory | 4 |
| AS.180.334 | Econometrics | 3 |
| Computer Science | ||
| EN.601.231 | Automata & Computation Theory | 3 |
| EN.601.433 | Intro Algorithms | 3 |
| EN.601.442 | Modern Cryptography | 3 |
| EN.601.457 | Computer Graphics | 3 |
| EN.601.461 | Computer Vision | 3 |
| EN.601.464 | Artificial Intelligence | 3 |
| EN.601.475 | Machine Learning | 3 |
| EN.601.476 | Machine Learning: Data to Models | 3 |
| Applied Mathematics and Statistics | ||
| EN.553.361 | Introduction to Optimization I | 4 |
| EN.553.362 | Introduction to Optimization II | 4 |
| EN.553.391 | Dynamical Systems | 4 |
| EN.553.420 | Probability | 4 |
| EN.553.426 | Introduction to Stochastic Processes | 4 |
| EN.553.430 | Mathematical Statistics | 4 |
| EN.553.453 | Mathematical Game Theory | 4 |
| EN.553.465 | Introduction to Convexity | 4 |
| EN.553.471 | Combinatorial Analysis | 4 |
| EN.553.472 | Graph Theory | 4 |
| EN.553.481 | Numerical Analysis | 4 |
| EN.553.492 | Mathematical Biology | 3 |
| EN.553.493 | Mathematical Image Analysis | 4 |
| Philosophy | ||
| AS.150.420 | Mathematical Logic I | 3 |
| AS.150.421 | Mathematical Logic II | 3 |
| AS.150.422 | Axiomatic Set Theory | 3 |
Sample Program of Study
The following chart is one example of how a student might progress through the mathematics major. As potential math majors enter JHU with a wide range of prior math abilities, students should begin courses at their current level of knowledge.
| First Year | |||
|---|---|---|---|
| First Semester | Credits | Second Semester | Credits |
| AS.110.108 | 4 | AS.110.109 | 4 |
| 4 | 4 | ||
| Second Year | |||
| First Semester | Credits | Second Semester | Credits |
| AS.110.202 or 211 | 4 | AS.110.201 or 212 | 4 |
| AS.110.302 (or other 300+ level elective) | 4 | ||
| 4 | 8 | ||
| Third Year | |||
| First Semester | Credits | Second Semester | Credits |
| AS.110.405 or 415 | 4 | AS.110.406 or 416 | 4 |
| Math application course | 3-4 | ||
| 7-8 | 4 | ||
| Fourth Year | |||
| First Semester | Credits | Second Semester | Credits |
| AS.110.401 | 4 | AS.110.304 | 4 |
| Math application course | 3-4 | ||
| 4 | 7-8 | ||
| Total Credits 42-44 | |||
Honors Program in Mathematics
As a general guideline, departmental honors are awarded to recipients of the B.A. degree who have completed the following with a combined GPA of at least 3.6 out of 4.0:
- both AS.110.411 Honors Algebra I and AS.110.412 Honors Algebra II,
- both AS.110.415 Honors Analysis I and AS.110.416 Honors Analysis II,
- either AS.110.407 Honors Complex Analysis or AS.110.607 Complex Variables,
- and one more course at the 400-level or above.
J.J. Sylvester Prize
The J.J. Sylvester Prize in Mathematics, which carries a cash award, is given each year to the one of two top-performing graduating seniors majoring in mathematics for outstanding achievement.
Undergraduate Teaching Assistantships
The department awards many upper-level undergraduates the opportunity to act as recitation instructors to our freshman courses. This award enables a student to practice the art of teaching and communicating mathematics in an environment where they are hired as a formal instructor to aid the professor of a regular curriculum course as a Teaching Assistant (TA). Undergraduate TAs are fully mentored and monitored, and the position provides a valuable credential and experience.
Undergraduate Learning Goals
At the time of graduation, math majors should:
- Have a good working knowledge of the language of mathematics as embodied in the basic constructs of mathematics in the fundamental areas of algebra, analysis, and geometry
- Be able to analyze the logical structure of a scientific or mathematical problem and to develop a meaningful approach to a solution
- Be able to read, understand, and construct a well-formed proof
- Develop the mathematical maturity and skills necessary to extend their knowledge through self-study and independent research
- Be able to apply mathematical methods to solve research problems arising outside of mathematics
- Be able to formulate precise mathematical statements and questions
- Be able to effectively and successfully communicate mathematics in both oral and written form to a broad mathematical and lay audience.