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Twin Cities Campus
Mathematics B.S.Math.
School of Mathematics
Institute of Technology
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Requirements for this program are current for Fall 2005.
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Required credits to graduate with this degree: 120.
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Required credits within the major: 56.
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Degree: Bachelor of Science in Mathematics.
The mission of the program is to provide high-quality mathematics instruction in a stimulating intellectual atmosphere. The goal is to educate students at all levels to provide cultural enrichment, to give them the analytic tools they need to become responsible citizens, and to prepare them for careers involving mathematics.
The School of Mathematics offers a program leading to the bachelor of science degree. The course of study is flexible and may be adapted to satisfy a wide variety of interests and needs. Students may prepare for graduate study in mathematics or emphasize various fields of interest, such as preparation for secondary school teaching, actuarial science, or programs in applied mathematics, including industrial mathematics, biology, mathematics applicable to computer science, and numerical analysis. Programs for specializations in actuarial science, preparation for teaching in the secondary school, and mathematics applicable to computer science earn a designation that appears on the diploma.
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Admission Requirements
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Students must complete 8 courses before admission to the program.
Freshmen and transfer students are usually admitted to pre-major status before admission to this major.
For information about University of Minnesota admission requirements, visit the
Office of Admissions Web site.
Mathematics
MATH 1271 - Calculus I, MATH (4.0 cr)
or MATH 1371 - IT Calculus I, MATH (4.0 cr)
MATH 1272 - Calculus II (4.0 cr)
or MATH 1372 - IT Calculus II (4.0 cr)
MATH 2243 - Linear Algebra and Differential Equations (4.0 cr)
or MATH 2373 - IT Linear Algebra and Differential Equations (4.0 cr)
MATH 2263 - Multivariable Calculus (4.0 cr)
or MATH 2374 - IT Multivariable Calculus and Vector Analysis (4.0 cr)
MATH 2283 - Sequences, Series, and Foundations (3.0 cr)
or MATH 3283W - Sequences, Series, and Foundations: Writing Intensive, WI (4.0 cr)
Physics
PHYS 1301W - Introductory Physics for Science and Engineering I, PHYS SCI/L, WI (4.0 cr)
or PHYS 1401V - Honors Physics I, PHYS SCI/L, WI, H (4.0 cr)
PHYS 1302W - Introductory Physics for Science and Engineering II, PHYS SCI/L, WI (4.0 cr)
or PHYS 1402V - Honors Physics II, PHYS SCI/L, WI, H (4.0 cr)
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General Requirements
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All students are required to complete general University and college
requirements including writing and liberal education courses.
For more information about University-wide requirements, see the
liberal education requirements.
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Program Requirements
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Students must complete eight upper division math courses at 4xxx or above and two technical elective courses, which can be mathematics courses.
The School of Mathematics will accept STAT 5101 and 5102 as part of the eight-course upper division mathematics requirement. The content of STAT 5101 is the same as MATH 5651. No other courses from other departments may be used as part of the eight-course math requirement, though other courses may be used as technical electives.
MATH 4512 may not be used to satisfy part of the eight course upper division math requirement, though it may be used as technical elective. MATH 3113, 3116, 3118, 4113, 4116, 4118, 3283W, and 4005 may not be used to satisfy part of the eight-course upper division math requirement or as technical electives.
In addition to the specializations described below, students who wish to pursue a pure mathemtics track or are planning to go to graduate school in mathematics should consult their adviser about appropriate course choices.
Specializations in Mathematics
Students are required to complete one of the following course groups.
Mathematics (No Specialization)
Students who do not choose one of the other specializations complete the basic requirements listed here. For the Technical Electives requirement, students must take at least 6 credits from courses that meet the following criteria: prerequisite of calculus; 3xxx or higher; courses form a coherent part of the student¿s program.
Take 2 or more course(s) from the following:
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Take 1 or more course(s) from the following:
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MATH 4281 - Introduction to Modern Algebra (4.0 cr)
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MATH 5248 - Cryptology and Number Theory (4.0 cr)
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MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
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MATH 5285H - Honors: Fundamental Structures of Algebra I, H (4.0 cr)
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MATH 5286H - Honors: Fundamental Structures of Algebra II, H (4.0 cr)
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MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
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Take 0 or more course(s) from the following:
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MATH 4242 - Applied Linear Algebra (4.0 cr)
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MATH 5705 - Enumerative Combinatorics (4.0 cr)
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MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
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MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
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MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
Depending on the specialization chosen, if any, students may be restricted in their choice of analys
Take 2 or more course(s) from the following:
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MATH 4606 - Advanced Calculus (4.0 cr)
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MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
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MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
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MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
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MATH 5583 - Complex Analysis (4.0 cr)
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MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
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MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
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MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
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MATH 5654 - Prediction and Filtering (4.0 cr)
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MATH 5615H - Honors: Introduction to Analysis I, H (4.0 cr)
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MATH 5616H - Honors: Introduction to Analysis II, H (4.0 cr)
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MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1107 - Introduction to FORTRAN Programming for Scientists and Engineers (3.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1901 - Structure of Computer Programming I (4.0 cr)
or CSCI 1902 - Structure of Computer Programming II (4.0 cr)
PHYS 2303 - Physics III: Physics of Matter (4.0 cr)
or PHYS 2311 - Modern Physics (4.0 cr)
or PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
Complete 6 credits of technical electives selected in consultation with your adviser.
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Mathematical Biology Specialization
Students select one of three options: environmental science, genomics, or physiology. Consult an adviser for more information.
MATH 4428 - Mathematical Modeling (4.0 cr)
MATH 4242 - Applied Linear Algebra (4.0 cr)
Take 1 or more course(s) from the following:
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MATH 4281 - Introduction to Modern Algebra (4.0 cr)
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MATH 5248 - Cryptology and Number Theory (4.0 cr)
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MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
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MATH 5285H - Honors: Fundamental Structures of Algebra I, H (4.0 cr)
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MATH 5286H - Honors: Fundamental Structures of Algebra II, H (4.0 cr)
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MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
BIOL 1009 - General Biology, BIOL SCI/L (4.0 cr)
or take the following course pair
BIOL 1001 - Introductory Biology I: Evolutionary and Ecological Perspectives, BIOL SCI/L, ENVT (4.0 cr)
BIOL 1002W {Inactive}
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1107 - Introduction to FORTRAN Programming for Scientists and Engineers (3.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1901 - Structure of Computer Programming I (4.0 cr)
or CSCI 1902 - Structure of Computer Programming II (4.0 cr)
MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
Senior seminar (1 credit)
Complete an approved research internship for at least four credits.
Complete the requirements for the environmental science or genomics or physiology option. See your adviser for specifics.
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Actuarial Specialization
Complete the requirements for the actuarial sub-plan.
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Mathematics Education Specialization
Complete the requirements for the mathematics education sub-plan.
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Computer Applications Specialization
Complete the requirements for the computer applications sub-plan.
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Program Sub-plans
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A sub-plan is not required for this program.
Actuarial Science
Students should take 6 courses of mathematics or statistics and math electives in economics, accounting, insurance, and finance.
For the computer science requirement, only 1103 or 1113 should be chosen. Math and Computer Science
These courses will fulfill both the analysis course requirement and one of the algebra course requirements.
MATH 4065 - Theory of Interest (3.0 cr)
MATH 5067 - Actuarial Mathematics I (4.0 cr)
MATH 5068 - Actuarial Mathematics II (4.0 cr)
MATH 4242 - Applied Linear Algebra (4.0 cr)
Take 1 or more course(s) from the following:
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MATH 4281 - Introduction to Modern Algebra (4.0 cr)
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MATH 5248 - Cryptology and Number Theory (4.0 cr)
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MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
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MATH 5285H - Honors: Fundamental Structures of Algebra I, H (4.0 cr)
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MATH 5286H - Honors: Fundamental Structures of Algebra II, H (4.0 cr)
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MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
or STAT 5102 - Theory of Statistics II (4.0 cr)
Economics and Business
1101-1102
ECON 1101 - Principles of Microeconomics, IP, SSCI (4.0 cr)
ECON 1102 - Principles of Macroeconomics, IP, SSCI (4.0 cr)
or 1104-05
ECON 1104 - Principles of Microeconomics, IP, SSCI (4.0 cr)
or ECON 1105 - Principles of Macroeconomics, IP, SSCI (4.0 cr)
ACCT 2050 - Introduction to Financial Reporting (4.0 cr)
ECON 3101 - Intermediate Microeconomics (4.0 cr)
FINA 3001 - Finance Fundamentals (3.0 cr)
ECON 4751 - Financial Economics (3.0 cr)
or FINA 4241 {Inactive}
Take 2 or more course(s) from the following:
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INS 4100 - Corporate Risk Management (2.0 cr)
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INS 4101 - Employee Benefits (2.0 cr)
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INS 4200 - Insurance Theory and Practice (2.0 cr)
Mathematics Education
Preparation for teaching in secondary education
Courses that are recommended but not required for this specialization include MATH 5652 Stochastic Processes or STAT 5102 Theory of Statistics II; and MATH 5336 Geometry II. IT majors can satisfy the technical elective requirement with courses in mathematics education. These may include two of MATHE 5011, MATHE 5021 and MATHE 5031, but the mathematics adviser should be consulted to approve the technical elective. Mathematics Education
These course fulfill the both the algebra and analysis requirements.
MATH 5335 - Geometry I (4.0 cr)
MATH 4242 - Applied Linear Algebra (4.0 cr)
or MATH 4281 - Introduction to Modern Algebra (4.0 cr)
or MATH 5285H - Honors: Fundamental Structures of Algebra I, H (4.0 cr)
MATH 4707 - Introduction to Combinatorics and Graph Theory (4.0 cr)
or MATH 5705 - Enumerative Combinatorics (4.0 cr)
or MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
Computer Science
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1107 - Introduction to FORTRAN Programming for Scientists and Engineers (3.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1901 - Structure of Computer Programming I (4.0 cr)
or CSCI 1902 - Structure of Computer Programming II (4.0 cr)
Physics
Take one of the following physics courses in the third semeser (fall semester of the second year).
PHYS 2303 - Physics III: Physics of Matter (4.0 cr)
or PHYS 2311 - Modern Physics (4.0 cr)
or PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
School Mathematics
Consult an adviser before completing this requirement.
Take 2 or more course(s) from the following:
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MTHE 5011 - Arithmetic Structures in School Mathematics (3.0 cr)
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MTHE 5021 - Algebraic Structures in School Mathematics (3.0 cr)
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MTHE 5031 - Geometric Structures in School Mathematics (3.0 cr)
Honors
This is an honors sub-plan.
For cum laude, students must complete a thesis and one honors experience and have a cumulative GPA of 3.50. To graduate magna cum laude, students must complete a thesis and two honors experiences and have a cumulative GPA of 3.66. For summa cum laude, students must complete a thesis and three honors experiences and have a cumulative GPA of 3.75. Consult an academic adviser for a list of possible honors experiences or to petition the department to approve an honors experience not listed.
Computer Applications
Take at least 24 credits of math/computer science courses relating to computer applications. Students who complete the computer application emphasis will also satisfy the requirements for a minor in computer science. Computer Applications
MATH 5486 may be used toward the analysis distribution requirement and MATH 5485 toward the algebra requirement.
CSCI 2011 - Discrete Structures of Computer Science (4.0 cr)
MATH 5165 - Mathematical Logic I (4.0 cr)
MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1901 - Structure of Computer Programming I (4.0 cr)
or CSCI 1902 - Structure of Computer Programming II (4.0 cr)
Additional Algebra
Take 1 or more course(s) from the following:
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MATH 4281 - Introduction to Modern Algebra (4.0 cr)
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MATH 5248 - Cryptology and Number Theory (4.0 cr)
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MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
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MATH 5285H - Honors: Fundamental Structures of Algebra I, H (4.0 cr)
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MATH 5286H - Honors: Fundamental Structures of Algebra II, H (4.0 cr)
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MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
Additional Analysis
Take 1 or more course(s) from the following:
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MATH 4606 - Advanced Calculus (4.0 cr)
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MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
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MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
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MATH 5583 - Complex Analysis (4.0 cr)
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MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
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MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
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MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
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MATH 5654 - Prediction and Filtering (4.0 cr)
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MATH 5615H - Honors: Introduction to Analysis I, H (4.0 cr)
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MATH 5616H - Honors: Introduction to Analysis II, H (4.0 cr)
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MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
Additional Computing-Related Mathematics
A course chosen from this group that also meets the algebra distribution requirement must be taken in addition to the two courses required for all majors.
MATH 4242 - Applied Linear Algebra (4.0 cr)
or MATH 5166 - Mathematical Logic II (4.0 cr)
or MATH 5248 - Cryptology and Number Theory (4.0 cr)
or MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
or MATH 5285H - Honors: Fundamental Structures of Algebra I, H (4.0 cr)
or MATH 5286H - Honors: Fundamental Structures of Algebra II, H (4.0 cr)
or MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
or MATH 5487 - Computational Methods for Differential and Integral Equations in Engineering and Science I (4.0 cr)
or MATH 5705 - Enumerative Combinatorics (4.0 cr)
or MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
or MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
Computer Science
Upper-level computer science courses may be counted as technical electives.
Take 3 or more course(s) from the following:
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CSCI 4041 - Algorithms and Data Structures (4.0 cr)
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CSCI 5107 - Fundamentals of Computer Graphics 1 (3.0 cr)
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CSCI 5108 - Fundamentals of Computer Graphics II (3.0 cr)
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CSCI 5403 - Computational Complexity (3.0 cr)
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CSCI 5421 - Advanced Algorithms and Data Structures (3.0 cr)
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CSCI 5511 - Artificial Intelligence I (3.0 cr)
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CSCI 5521 - Pattern Recognition (3.0 cr)
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CSCI 8442 - Computational Geometry and Applications (3.0 cr)
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CSCI 5512W {Inactive}
or CSCI 5512 - Artificial Intelligence II (3.0 cr)
Physics
A physics course from the following list should be taken in the third semester (fall semester of the second year).
PHYS 2303 - Physics III: Physics of Matter (4.0 cr)
or PHYS 2311 - Modern Physics (4.0 cr)
or PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
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