## Sample Master's Degree Programs of Study

The following pages provide examples of programs of study in the 4 specializations for the M.S. in mathematics (10 courses, 30 hours). Many other combinations of courses are possible. The sequences below are suggested for full-time graduate students. Part-time graduate students should consult with an adviser for an appropriate schedule. Your adviser will have up-to-date information on the semesters when particular courses are normally offered.

See the NIU Graduate Catalog for course descriptions (scroll down to Mathematical Sciences) and detailed information on degree requirements.

 Average Background Strong Background 1st term, Year One MATH 520* Algebra I 1st term, Year One MATH 630 Real Analysis I MATH 530* Advanced Calculus I MATH 636 Ordinary Differential Equations I Computer Science 230* FORTRAN MATH 662 Numerical Analysis 2nd term, Year One MATH 523 Linear and Multilinear Algebra 2nd term, Year Two MATH 523 Linear and Multilinear Algebra MATH 531 Advanced Calculus II MATH 632 Complex Analysis Elective MATH 642 Partial Differential Equations I 1st term, Year Two MATH 630 Real Analysis I 1st term, Year Two MATH 620 Algebraic Structures I MATH 636 Ordinary Differential Equations I MATH 631 Functional Analysis MATH 662 Numerical Analysis MATH 640 Applied Mathematics 2nd term, Year Two MATH 632 Complex Analysis 2nd term, Year Two Electives (621, 664, 666, 684, or 700 level) MATH 642 Partial Differential Equations (or MATH 542) Elective (664, 666, or 684) Year Two --- M.S. Written Comprehensive Examination on Analysis and Differential Equations **

 Average Background Strong Background 1st term, Year One MATH 520* Algebra I 1st term Year One MATH 630 Real Analysis I MATH 530* Advanced Calculus I MATH 662 Numerical Analysis MATH 534 Numerical Linear Algebra MATH 668 Nonlinear Programming 2nd term, Year Two MATH 523 Linear and Multilinear Algebra 2nd term, Year Two MATH 523 Linear and Multilinear Algebra MATH 531 Advanced Calculus II MATH 664 Numerical Linear Algebra MATH 535 Numerical Analysis MATH 666 Numerical Differential Equations 1st term, Year Two MATH 630 Real Analysis I 1st term, Year Two MATH 631 Functional Analysis MATH 636 Ordinary Differential Equations I MATH 636 Ordinary Differential Equations I MATH 668 Nonlinear Programming Elective 2nd term, Year Two MATH 664 Numerical Linear Algebra 2nd term, Year Two MATH 632 Complex Analysis MATH 666 Numerical Differential Equations Elective Elective Elective Year Two --- M.S. Written Comprehensive Examination on Analysis and Numerical Mathematics **

III. M.S. in Mathematics: Mathematics Education Specialization
Average Background Strong Background

1st term, Year One MATH 520* Algebra I 1st term, Year One MATH 610 Theoretical Foundations of Mathematics Education
MATH 530* Advanced Calculus I MATH 613 Teaching of Algebra
MATH 610 Theoretical Foundations of Mathematics Education MATH 620 Algebraic Structures I
2nd term, Year One MATH 521 Algebra II 2nd term, Year One MATH 523 Linear and Multilinear Algebra
MATH 531 Advanced Calculus II MATH 531 Advanced Calculus II
MATH 614 Teaching of Geometry MATH 614 Teaching of Geometry

1st term, Year Two MATH 480 Number Theory 1st term, Year Two Stat 573/573A Statistical Methods and Models I
MATH 613 Teaching of Algebra MATH 630 Real Analysis I
MATH 620 Algebraic Structures I (or MATH 630 Real Analysis I) Graduate course in a related discipline such as education, psychology ... with consent of the adviser.
2nd term, Year Two STAT 573/573A Statistical Methods and Models I (or MATH 632 Complex Analysis) 2nd term, Year Two MATH 611 Introduction to Mathematics Education Research
MATH 611 Introduction to Mathematics Education Research MATH 632 Complex Analysis
Graduate course in a related discipline such as education, psychology ... with consent of the adviser. Graduate course in a related discipline such as education, psychology ... with consent of the adviser.
Year Two --- M.S. Written Comprehensive Examination over Algebra (or Analysis) and Mathematics Education **

 Average Background Strong Background 1st term, Year One MATH 520* Algebra I 1st term, Year One MATH 620 Algebraic Structures I MATH 530* Advanced Calculus I MATH 630 Real Analysis I MATH 534 Numerical Linear Algebra MATH 636 Ordinary Differential Equations I 2nd term, Year One MATH 521 Algebra 2nd term, Year One MATH 621 Algebraic Structures II MATH 523 Linear and Multilinear Algebra MATH 632 Complex Analysis MATH 531 Advanced Calculus II MATH 650 Topology 1st term, Year Two MATH 620 Algebraic Structures I 1st term, Year Two MATH 631 Functional Analysis MATH 630 Real Analysis I MATH 662 Numerical Analysis MATH 636 Ordinary Differential Equations I Elective 2nd term, Year Two MATH 535 Numerical Analysis 2nd term, Year Two Elective MATH 632 Complex Analysis Elective MATH 650 Topology or MATH 521 Algebraic Structures II Elective
Year Two:   M.S. Written Comprehensive Examination over Algebra and Analysis **

Notes for sample master's programs (Items I--IV): (*) Both MATH 520 and MATH 530 carry graduate credit, but only one of them may be counted toward a graduate degree in mathematics. Also, Computer Science 230 does not count toward the graduate program.

(**) With the consent of the department, master's students have the option of writing a master's thesis, instead of passing a written comprehensive examination. The thesis is prepared under the direction of a member of the graduate faculty, and is defended during an oral comprehensive examination. In most cases the thesis experience leads to three hours of credit in MATH 699, which can be applied to the 30 hours required for the master's degree.