Scientific Computing & Applied Mathematics Curriculum
Students in the SciCAM program must demonstrate mastery in the foundations of scientific computing and applied mathematics, either by producing evidence through undergraduate transcripts, or by taking some or all of the following foundational courses before or upon entry to the M.S. program:
AM 129 or AM 209: Foundations of Scientific Computing
Students cannot receive credit for AM 129 and AM 209. Students with any undergraduate major in the Baskin School of Engineering can request waivers for AM 129/209.
AM 147: Computational Methods and Applications
Students with an undergraduate major in Mathematics can request a waiver of AM 147 if they have taken MATH 148 or its equivalent. Students with an undergraduate major in Physics or Astrophysics can request a waiver of AM 147 if they have taken PHYS 115 or ASTR 119.
AM 100 or AM 211: Foundations of Applied Mathematics
Students with an undergraduate major in Mathematics can request a waiver of AM 211 if they have taken MATH 107 or its equivalent. Students with an undergraduate major in Physics or Astrophysics can request a waiver of AM 211 if they have taken the PHYS 116A/B/C series or its equivalent.
All SciCAM M.S. students are required to take the core courses listed below.
- AM 212A: Applied Mathematical Methods I
- AM 213A: Numerical Linear Algebra
- AM 213B: Numerical Methods for the Solution of Differential Equations
- AM 214: Applied Dynamical Systems
- AM 250: An Introduction to High Performance Computing
All non-seminar core courses must be taken for letter grades.
Any 5-credit AM graduate course (200 and above) not already listed as a core course may be counted as electives. Elective courses outside of AM must be approved by the SciCAM graduate director. Note that some upper-division electives are allowed, bearing in mind that no more than a total of 15 credits of upper-division courses may be used to satisfy the degree requirements.
Students in the SciCAM program may pursue a Plan I thesis or Plan II capstone (comprehensive examination) curriculum.
Candidates for a Plan I thesis must complete one elective and take a minimum of two quarters of independent study to write a thesis.
The thesis requirements are as follows. Students must submit a thesis proposal to the potential faculty sponsor after completion of all core courses. If the proposal is accepted, the faculty member will become the sponsor and will supervise the research and writing of the thesis project. The project will involve the solution of a problem or problems from the selected area of application. The thesis must consist of at least 30 pages and no more than 60 pages of printed written work and accompanying pertinent figures, consisting of a coherent introduction and presentation of the current state of the field, a clear presentation of the questions raised, of the methodology used to solve them, and a discussion of the results obtained. The thesis will be read by a committee of three ladder-rank faculty members, consisting of the faculty adviser and two additional readers. Additional readers will be chosen appropriately from within the Applied Mathematics Department or outside of it. At least two members of the reading committee must be from within the Applied Mathematics Department. The student will then be required to give a short (20-minute) public oral presentation of their thesis, which will be evaluated by the reading committee. The reading committee will assess the quality of both written work and oral presentation in making their recommendation for awarding the M.S. degree to the student.
Candidates for a Plan II capstone (comprehensive examination) must complete three electives and pass the SciCAM comprehensive examination.
The exam takes place in June at the end of the academic year. Students may only take this exam following completion of the last core course. The exam will take the form of a take-home exam covering all core and foundational courses. Passing the comprehensive examination fulfills the capstone requirement. A student will have two attempts to pass the exam.
NOTE: This is an abbreviated version of the program requirements. Please review the Program Statement for a full explanation of all program requirements.
The ability to take a real-life science or engineering problem, and create a mathematical model of it, under supervision or with the help of discussions with colleagues.
Proficiency in analytical methods for the solution of linear algebra problems, ordinary and partial differential equations.
Proficiency in the construction of numerical algorithms for the solution of linear algebra problems, as well as ordinary and partial differential equations.
Proficiency in at least two scientific computing languages such as Fortran, C, Python, R, Matlab, etc. Familiarity with Unix-type operating systems, the use of compilers, professional scientific computing libraries, efficient I/O algorithms, data visualization tools, etc.
Proficiency in the two main parallel computing paradigms (shared vs. distributed memory) and in the use of OpenMP and MPI. Familiarity with parallel architectures and with supercomputing environments such as batch submission scripts, data transfer protocols, scripting, etc.
The ability to identify and implement, among all of the existing methods and languages, the most appropriate and efficient approach for the problem posed.
The ability to analyze the results critically from the model obtained, and to present them to peers in a clear and coherent way in a form of scientific writing and oral presentation.