# Concentration in Scientific Computing

Scientific Computing is the collection of tools, techniques, and theories required to solve, on a computer, mathematical models of problems in Science and Engineering. Scientific Computing focuses on providing a fully interpretable generative process (model) based on physical laws which govern the system under study. Modeling and simulation can be used to verify hypotheses, make predictions, and drive experimental data collection. This Scientific Computing concentration of the major in ACMS provides students with (i) solid programming background for running computer simulations, (ii) computing and modeling courses for learning how to develop mathematical models, (iii) foundational methods courses for learning how to analyze the stability and accuracy of computer simulations, and (iv) elective courses to explore additional topics or applications of scientific computing.

The required courses for this concentration are as follows:

- 3 credits from Second Course in Scientific Computing
- 6 credits arising from additional electives chosen from either Second Course in Scientific Computing, Foundational Methods, Computing and Modeling, or Additional Electives lists

**Second Course in Scientific Computing**

- Scientific Programming (ACMS 40210)
- Advanced Scientific Computing (ACMS 40212)

**Foundational Methods**

- Numerical Linear Algebra (ACMS 40395)
- Applied Complex Analysis (ACMS 40485/50485)
- Nonlinear and Stochastic Optimization (ACMS/CBE 40499)
- Computational Methods (AME 30125)
- Chemical Process Control (CBE 30338)

**Computing and Modeling**

- Finite Element Methods (ACMS/AME 40541)
- Nonlinear Dynamical Systems (ACMS 40630)
- Artificial Neural Networks (ACMS 40640)
- Mathematical/Comp Modeling (ACMS 40730)
- Mathematical/Comp Modeling in Neuroscience (ACMS 40740)
- Introduction to Stochastic Modeling (ACMS 40760)
- Stochastic Simulation Algorithms (ACMS 40770)
- Computational Statistics (ACMS 40878)
- Computational Fluid Dynamics (ACMS 40532)
- Introduction to Biocomputing (BIOS 30318)
- Epidemiology and Ecology of Infectious Diseases (BIOS 40427)
- Molecular Modeling & Simulation (CBE 40475)
- Machine Learning for Chemical Engineers (CBE 40501)
- Computational Chemistry I (CHEM 40650)

**Additional Elective**

- Mathematical Cryptography with Python (ACMS 40100)
- Partial Differential Equations (ACMS/MATH 40750)
- Bayesian Statistics & Biological Forecasting (BIOS 40552)
- Process Operations (CBE 40455)

## ACMS/Scientific Computing Sample Curriculum:

**First Year**

First Semester | Second Semester | ||
---|---|---|---|

MATH 10550. Calculus I | 4 | MATH 10560. Calculus II | 4 |

CHEM 10171. Chemical Principles | 4 | CHEM 10172 or 10122 | |

PHYS 10310. General Physics I | 4 | PHYS 10320. General Physics II | 4 |

History or Social Science | 3 | Philosophy or Theology | 3 |

WR 13x00. Writing | 3 | University Seminar | 3 |

FYS 10101. First Year Experience | 1 | FYS | 1 |

Total Credits |
19 |
Total Credits |
19 |

**Sophomore Year**

First Semester | Second Semester | ||
---|---|---|---|

ACMS 20550. Applied Math Methods I | 3.5 | ACMS 20750. Applied Math Methods II | 3.5 |

ACMS 20620. Applied Linear Algebra/ ACMS Scientific Computing | 3/3.5 | ACMS 20620. Applied Linear Algebra/ ACMS Scientific Computing | 3/3.5 |

Language | 3 | ACMS 30530. Introduction to Probability | 3 |

Philosophy or Theology | 3 | Language | 3 |

Elective | 3 | Philosophy or Theology | 3 |

Total Credits |
15.5/16 |
Total Credits |
15.5/16 |

**Junior Year**

First Semester | Second Semester | ||
---|---|---|---|

ACMS 30600. Stat. Mthd & Data Analysis I | 3.5 | ACMS Elective | 3 |

ACMS 40390. Numerical Analysis/ (ACMS 40730. Math/Comp Modeling/ACMS 40760 Stochastic Modeling)** | 3 | ACMS 40390. Numerical Analysis/ (ACMS 40730. Math/Comp Modeling/ ACMS 40740 Math/Comp Modeling in neuroscience)** | 3 |

Language | 3 | Literature or Fine Arts | 3 |

Philosophy or Theology | 3 | Science Elective | 3 |

Elective | 3 | ACMS 40210 (SC Concentration) | 3 |

Total Credits |
15.5 |
Total Credits |
15 |

**One of the ACMS 40730, 40740, 40760 will satisfy the modeling course requirement. If two or more courses are taken, the other can be counted as ACMS elective. At least one of the three courses will be offered each semester.

**Senior Year**

First Semester | Second Semester | ||
---|---|---|---|

ACMS Elective | 3 | ACMS Elective | 3 |

SC Concentration (Foundational Methods) | 3 | SC Concentration (Elective) | 3 |

Electives | 9 | Electives | 6 |

Total Credits |
15 |
Total Credits |
12 |

**Notes:**

- Equivalent or higher sequences in science may be substituted, e.g., MATH 10850, 10860 for MATH 10550, 10560.
- Some ACMS courses, ACMS 30440 in particular, are not acceptable as electives for the major. The list of acceptable courses for ACMS majors can be obtained from the student’s advisor. Introduction to Mathematical Reasoning (MATH 20630) is also an acceptable elective.
- Students with an interest in attending graduate school in mathematics or applied mathematics are encouraged to take Algebra (MATH 30710).
- An appropriate class in bioinformatics, biophysics, or a related topic, may be substituted for 3 credits in ACMS coursework with the permission of the Director of Undergraduate Studies.
- A student should take three core requirement courses during the first year, including one course that is designated a University Seminar. It is recommended that one course in history or social sciences be taken in the first year and one philosophy and one theology be taken by the end of sophomore year.

## STAT/Scientific Computing Sample Curriculum:

**First Year**

**First Year**First Semester | Second Semester | ||
---|---|---|---|

Math 10550. Calculus I | 4 | MATH 10560. Calculus II | 4 |

CHEM 10171. Chemical Principles | 4 | CHEM 10172 or 10122 | 4 |

PHYS 10310. General Physics I | 4 | PHYS 10320. General Physics II | 4 |

History or Social Science | 3 | Philosophy or Theology | 3 |

WR 13x00. Writing | 3 | University Seminar | 3 |

FYS 10101. First Year Experience | 1 | FYS | 1 |

Total Credits |
19 |
Total Credits |
19 |

**Sophomore Year**

First Semester | Second Semester | ||
---|---|---|---|

ACMS 20550. Applied Math Methods I | 3.5 | ACMS 20750. Applied MathMethods II | 3.5 |

ACMS 20620. Applied Linear Algebra/ ACMS Scientific Computing | 3/3.5 | ACMS 20620. Applied Linear Algebra/ ACMS Scientific Computing | 3/3.5 |

Elective | 3 | ACMS 30530. Introduction to Probability | 3 |

Philosophy or Theology | 3 | Language | 3 |

Language | 3 | Philosophy or Theology | 3 |

Total Credits |
15.5/16 |
Total Credits |
15.5/16 |

### Junior Year

First Semester | Second Semester | ||
---|---|---|---|

ACMS 30600. Stat Mthd & Data Analysis I |
3.5 | ACMS Statistics Elective | 3 |

ACMS 40390. Numerical Analysis*/ ACMS/MATH Elective | 3 | ACMS 40210 (Sci Comp) | 3 |

Language | 3 | Literature or Fine Arts | 3 |

Science Elective | 3 | Philosophy or Theology | 3 |

Elective | 3 | ACMS Statistics Elective | 3 |

Total Credits |
15.5 |
Total Credits |
15 |

*ACMS 40390 is a suggested elective, but it can be replaced by other ACMS/MATH elective.

### Senior Year

First Semester | Second Semester | ||
---|---|---|---|

ACMS 30550. Mathematical Statistics | 3 | ACMS Statistics Elective | 3 |

Sci Comp Concentration (Computing and Modeling) | 3 | Electives | 9 |

Sci Comp Concentration (Elective) | 3 | ||

Electives | 6 | ||

Total Credits |
15 |
Total Credits |
12 |

- Equivalent or higher sequences in science may be substituted, e.g., MATH 10850, 10860 for MATH 10550, 10560.
- The acceptable elective courses are:
- ACMS 30810 Design of Experiments
- ACMS 40842 Time Series Analysis
- ACMS 40852 Advanced Biostatistical Methods
- ACMS 40855 Spatio-Temporal Statistics
- ACMS 40875 Statistical Methods in Data Mining
- ACMS 40878 Statistical Computing with R
- ACMS 40950 Topics in Statistics
- Any graduate ACMS course in statistics or probability

- Introduction to Mathematical Reasoning (MATH 20630) is also an acceptable elective.
- A student should take three core requirement courses during the first year, including one course that is designated a University Seminar. It is recommended that one course in history or social sciences be taken in the first year and one philosophy and one theology be taken by the end of sophomore year.