Kroschel, Brenda
Professional Interests
structured eigenvectors
interlacing
matrix completions
totally nonnegative matrices
zero forcing number
Twin Cities Math Teachers' Circle
I received my PhD in Matrix Theory from the College of William and Mary. Prior to that I worked in industry for a number of years including three years for an options and futures trading firm in the Chicago Board of Trade. My research interests include matrix completion problems, eigenvalue interlacing, structured eigenvectors, totally nonnegative matrices,and zero forcing number.
I am one of the coorganizers of Minnesota's first Math Teachers' Circle called the Twin Cities Math Teachers' Circle (TCMTC). Myself, Melissa Loe and Cheri Shakiban from University of St. Thomas together with Minneapolis middle school teachers Patty DeJarLais and Chris Wernimont started the circle in August 2010. There are currently 18 members of the TCMTC and we meet each month to work on interesting math problems and improve the problem solving skills of the middle school math teachers who are members. We hope to energize these teachers so they bring their enthusiasm and improved problem solving skills back to their classrooms.
Education:
 Ph.D., Applied Science Program ( Mathematics Track) College of William and Mary, 1996.
 M.S., Mathematical Sciences, Clemson University, 1987 .
 B.A., Mathematics and Chemistry, St. Olaf College, 1985.
Publications:
 Principal Submatrices, Geometric Multiplicities, and Structured Eigenvectors, C.R. Johnson, and B.K. Kroschel, SIAM J. Matrix Anal. Appl, 163 (1995) 10041012.
 The Euclidean Distance Completion Problem: Cycle Completability, C.R. Johnson, C.A. Jones, and B.K. Kroschel, Linear and Multilinear Algebra, 39 (1995) 195207.
 An InteriorPoint Method for Approximate Positive Semidefinite Completions, C.R. Johnson, B.K. Kroschel, and H. Wolkowicz, Computational Optimization and Applications, accepted.
 Extended Interlacing Intervals, C.R. Johnson, R.O. Hill, and B.K. Kroschel, Linear Algebra and its Applications, accepted.
 The "Clock Hands" Computer Graphics Program, C.R. Johnson and B.K. Kroschel, College Journal of Mathematics, to appear.
 The Pmatrix Completion Problem, C.R. Johnson and B.K. Kroschel, Electronic Journal of Linear Algebra, vol 1.
 The Totally Nonnegative Completion Problem, C.R. Johnson, B.K. Kroschel, and M. Lundquist, Fields Institute Communications, to appear.
Spring 2018 Courses
Course  Section  Title  

MATH 113  01  Calculus I  
Description of course Genetics B/ Lab: 
Course Registration Number:20161 (View in ClassFinder) Credit Hours:4 Credit Hours Instructor:Brenda K. Kroschel An introductory course in calculus: limits; derivatives and integrals of algebraic, exponential, logarithmic and trigonometric functions of one real variable; applications of the derivative in engineering and the natural sciences. Offered Fall, Spring and Summer. Prerequisite: a grade of C or above in MATH 105 or placement at MATH 113 or above. Four years of high school mathematics, including college algebra and trigonometry, also are recommended as background for this course. NOTE: Students who receive credit for MATH 113 may not receive credit for MATH 108, 109, or 111. Schedule Details


MATH 113  02  Calculus I  
Description of course Genetics B/ Lab: 
Course Registration Number:20162 (View in ClassFinder) Credit Hours:4 Credit Hours Instructor:Brenda K. Kroschel An introductory course in calculus: limits; derivatives and integrals of algebraic, exponential, logarithmic and trigonometric functions of one real variable; applications of the derivative in engineering and the natural sciences. Offered Fall, Spring and Summer. Prerequisite: a grade of C or above in MATH 105 or placement at MATH 113 or above. Four years of high school mathematics, including college algebra and trigonometry, also are recommended as background for this course. NOTE: Students who receive credit for MATH 113 may not receive credit for MATH 108, 109, or 111. Schedule Details


MATH 301  01  Abstract Algebra I  
Description of course Genetics B/ Lab: 
Course Registration Number:20854 (View in ClassFinder) Credit Hours:4 Credit Hours Instructor:Brenda K. Kroschel Properties of sets, relations and mappings; introduction to groups, rings and fields. Offered Spring. Prerequisite: A grade of C or above in MATH 240 Schedule Details

Summer 2018 Courses
Course  Section  Title 

Fall 2018 Courses
Course  Section  Title  

MATH 114  02  Calculus II  
Description of course Genetics B/ Lab: 
Course Registration Number:40232 (View in ClassFinder) Credit Hours:4 Credit Hours Instructor:Brenda K. Kroschel Techniques of integration; applications of integration; infinite series; parametric/polar equations. Offered Fall, Spring and Summer. Prerequisite: a grade of C or above in MATH 112 or in MATH 113 or MATH 109 Schedule Details


MATH 114  03  Calculus II  
Description of course Genetics B/ Lab: 
Course Registration Number:40838 (View in ClassFinder) Credit Hours:4 Credit Hours Instructor:Brenda K. Kroschel Techniques of integration; applications of integration; infinite series; parametric/polar equations. Offered Fall, Spring and Summer. Prerequisite: a grade of C or above in MATH 112 or in MATH 113 or MATH 109 Schedule Details


MATH 210  03  IntroDiffer Equations & Syst  
Description of course Genetics B/ Lab: 
Course Registration Number:41179 (View in ClassFinder) Credit Hours:4 Credit Hours Instructor:Brenda K. Kroschel An introduction to ordinary differential equations (ODEs), with an emphasis on linear differential equations and linear systems, including applications. Topics covered include firstorder equations, ODE models in the physical and biological sciences and engineering, numerical methods of solution, higher order linear equations, matrix tools, the role of eigenvalues and eigenvectors, and LaPlace transforms. Offered Fall and Spring. Prerequisite: a grade of C or above in MATH 114 Schedule Details
