Applied Mathematics & Statistics - (2021-2022 Catalog) 1 Specialty in Computational & Applied Applied Mathematics & Mathematics Statistics Required Courses MATH500 LINEAR VECTOR SPACES 3.0 Degrees Offered MATH514 APPLIED MATHEMATICS I 3.0 • Master of Science (Applied Mathematics and Statistics) MATH515 APPLIED MATHEMATICS II 3.0 • Doctor of Philosophy (Applied Mathematics and Statistics) MATH550 NUMERICAL SOLUTION OF PARTIAL 3.0 DIFFERENTIAL EQUATIONS Program Description MATH551 COMPUTATIONAL LINEAR ALGEBRA 3.0 The Department of Applied Mathematics and Statistics (AMS) at SYGN502 INTRODUCTION TO RESEARCH ETHICS * 1.0 Colorado School of Mines prepares the next generation of mathematical MATH589 APPLIED MATHEMATICS AND STATISTICS 1.0 and statistical scientists to be leaders in a world driven by increasingly TEACHING SEMINAR ** complex technology and challenges. Our department is at the forefront of research in mathematical and statistical methods that are used *Required only for students receiving federal support. to address the opportunities and challenges of the future. The AMS ** Required only for students employed by the department as graduate department offers two graduate degrees: A Master of Science in Applied teaching assistants or student instructor/lecturers. Mathematics and Statistics and a Doctor of Philosophy in Applied Mathematics and Statistics. The master's program is designed to prepare Furthermore, students are required to complete two additional MATH candidates for careers in industry or government or for further study courses, either at the 500-level or chosen from the following 400-level at the PhD level. The PhD program is sufficiently flexible to prepare courses. candidates for careers in industry, government and academia. A course MATH Elective Courses (400-level) of study leading to the PhD degree can be designed either for students who have completed a Master of Science degree or for students with a MATH408 COMPUTATIONAL METHODS FOR 3.0 Bachelor of Science degree. DIFFERENTIAL EQUATIONS MATH454 COMPLEX ANALYSIS 3.0 The AMS department is also involved in the curriculum of three MATH455 PARTIAL DIFFERENTIAL EQUATIONS 3.0 different interdisciplinary master's degree programs: Data Science, MATH458 ABSTRACT ALGEBRA 3.0 Operations Research with Engineering, and Quantitative Biosciences and Engineering. Please view "Interdisciplinary Programs" for more MATH484 MATHEMATICAL AND COMPUTATIONAL 4.0 information on these programs. MODELING (CAPSTONE) Research within AMS is conducted in the following areas: Finally, the remaining nine credits come from general elective courses and may be selected from any other graduate courses offered by the Computational and Applied Mathematics Department of Applied Mathematics and Statistics, except for specially Wave Phenomena and Inverse Problems designated service courses. Alternatively, up to 6 credits of elective Numerical Methods for PDEs courses may be taken in other departments on campus to satisfy this Differential and Integral Equations requirement. Multi-scale Analysis and Simulation High Performance Scientific Computing Specialty in Statistics Dynamical Systems Required Courses Mathematical Biology Meshfree Approximation Methods MATH500 LINEAR VECTOR SPACES 3.0 MATH531 THEORY OF LINEAR MODELS 3.0 Statistics MATH534 MATHEMATICAL STATISTICS I 3.0 Geophysical and Environmental Applications Methods for Massive Data Sets MATH535 MATHEMATICAL STATISTICS II 3.0 Spatial and Space-Time Processes MATH560 INTRODUCTION TO KEY STATISTICAL 3.0 Functional Data Analysis LEARNING METHODS I Inverse Problems MATH589 APPLIED MATHEMATICS AND STATISTICS 1.0 Uncertainty Quantification TEACHING SEMINAR ** SYGN502 INTRODUCTION TO RESEARCH ETHICS * 1.0 Master of Science Program Requirements *Required only for students receiving federal support. The Master of Science degree (non-thesis option) requires 30 credit ** Required only for students employed by the department as graduate hours of coursework. Students pursuing the degree may count up to teaching assistants or student instructor/lecturers. six credits from courses at the 400-level. For both the Computational & Applied Mathematics and Statistics specialties, the curriculum structure Furthermore, students are required to complete two additional MATH consists of (i) a set of required courses, (ii) a pair of MATH electives, courses, either at the 500-level or chosen from the following 400-level and (iii) general elective courses that serve to supplement the student's courses. technical interests. 2 Applied Mathematics & Statistics - (2021-2022 Catalog) MATH Elective Courses (400-level) MATH551 COMPUTATIONAL LINEAR ALGEBRA 3.0 * MATH408 COMPUTATIONAL METHODS FOR 3.0 SYGN502 INTRODUCTION TO RESEARCH ETHICS 1.0 DIFFERENTIAL EQUATIONS MATH589 APPLIED MATHEMATICS AND STATISTICS 1.0 ** MATH454 COMPLEX ANALYSIS 3.0 TEACHING SEMINAR MATH455 PARTIAL DIFFERENTIAL EQUATIONS 3.0 MATH588 INTRODUCTION TO QUANTITATIVE AND 1.0 MATH458 ABSTRACT ALGEBRA 3.0 COMPUTATIONAL RESEARCH MATH484 MATHEMATICAL AND COMPUTATIONAL 4.0 *Required only for students receiving federal support. MODELING (CAPSTONE) ** Required only for students employed by the department as graduate teaching assistants or student instructor/lecturers. Finally, the remaining nine credits come from general elective courses and may be selected from any other graduate courses offered by the Furthermore, students are required to complete two additional MATH Department of Applied Mathematics and Statistics, except for specially courses, either at the 500-level or chosen from the following 400-level designated service courses. Alternatively, up to 6 credits of elective courses. courses may be taken in other departments on campus to satisfy this requirement. MATH Elective Courses (400-level) MATH408 COMPUTATIONAL METHODS FOR 3.0 The Master of Science degree (thesis option) requires 30 credit DIFFERENTIAL EQUATIONS hours of acceptable coursework and research, completion of a satisfactory thesis, and successful oral defense of this thesis. A MATH454 COMPLEX ANALYSIS 3.0 minimum of 6 (and a maximum of 12) of the 30 credit hours must MATH455 PARTIAL DIFFERENTIAL EQUATIONS 3.0 be designated for supervised research, which will be in lieu of MATH458 ABSTRACT ALGEBRA 3.0 electives. The coursework includes the required core curriculum for MATH484 MATHEMATICAL AND COMPUTATIONAL 3.0 the chosen specialty described above. MODELING (CAPSTONE) Mines Combined Undergraduate / Graduate Specialty in Statistics Degree Program Required Courses The Department of Applied Mathematics and Statistics offers a combined MATH500 LINEAR VECTOR SPACES 3.0 Bachelor of Science/Master of Science program that enables students to work on a Bachelor of Science and a Master of Science in either MATH531 THEORY OF LINEAR MODELS 3.0 specialty simultaneously. Students take 30 credit hours of coursework MATH534 MATHEMATICAL STATISTICS I 3.0 at the graduate level in addition to the undergraduate requirements, and MATH535 MATHEMATICAL STATISTICS II 3.0 work on both degrees at the same time. As described above, students MATH560 INTRODUCTION TO KEY STATISTICAL 3.0 pursuing the Master of Science degree may count up to six credits LEARNING METHODS I from courses at the 400-level. Additionally, students enrolled within the MATH588 INTRODUCTION TO QUANTITATIVE AND 1.0 combined program may choose up to six credits of MATH coursework COMPUTATIONAL RESEARCH at the 500-level (that has been successfully completed with a grade of MATH589 APPLIED MATHEMATICS AND STATISTICS 1.0 B or above) to "double-count"; that is, apply towards both their Bachelor TEACHING SEMINAR ** of Science degree requirements and their Master of Science degree * requirements simultaneously. Interested students are encouraged to SYGN502 INTRODUCTION TO RESEARCH ETHICS 1.0 apply for the combined program once they have completed five classes with a MATH prefix numbered 225 or higher. *Required only for students receiving federal support. ** Required only for students employed by the department as graduate Doctor of Philosophy Program Requirements teaching assistants or student instructor/lecturers. The Doctor of Philosophy requires 72 credit hours beyond the bachelor’s Furthermore, students are required to complete two additional MATH degree. At least 24 of these hours must be thesis hours. Students courses, either at the 500-level or chosen from the following 400-level pursuing the degree may count up to six credits from courses at the 400- courses. level. Doctoral students must pass the comprehensive examination (a qualifying examination and thesis proposal), complete a satisfactory MATH Elective Courses (400-level) thesis, and successfully defend their thesis. MATH408 COMPUTATIONAL METHODS FOR 3.0 DIFFERENTIAL EQUATIONS Specialty in Computational & Applied MATH454 COMPLEX ANALYSIS 3.0 Mathematics MATH455 PARTIAL DIFFERENTIAL EQUATIONS 3.0 Required Courses MATH458 ABSTRACT ALGEBRA 3.0 MATH500 LINEAR VECTOR SPACES 3.0 MATH484 MATHEMATICAL AND COMPUTATIONAL 3.0 MATH514 APPLIED MATHEMATICS I 3.0 MODELING (CAPSTONE) MATH515 APPLIED MATHEMATICS II 3.0 Further information can be found on the Web at ams.mines.edu. MATH550 NUMERICAL SOLUTION OF PARTIAL 3.0 This website provides an overview of the programs, requirements, DIFFERENTIAL EQUATIONS and policies of the department. Applied Mathematics & Statistics - (2021-2022 Catalog) 3 Fields of Research: MATH503. FUNCTIONAL ANALYSIS. 3.0 Semester Hrs. (II) Properties of metric spaces, normed spaces and Banach spaces, Geophysical and Environmental