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Linda Patton

Linda Patton

Professor

Email: lpatton@calpoly.edu
Office Phone: 805-756-1680
Office: 25-323

Office Hours

Education

1991 Ph.D. in Mathematics, University of California at San Diego, La Jolla, California
1987 M.A. in Mathematics, University of California at San Diego, La Jolla, California
1985 B.A. in Applied Mathematics, University of California at San Diego, La Jolla, California

About

I have been teaching in the Cal Poly Mathematics Department since 1991. My research interests are in operator theory; some particular interests are numerical ranges of operators, composition operators on spaces of analytic functions, Pick interpolation, and other topics where matrix theory and function theory interact.

I particularly enjoy research with Cal Poly undergraduates and Master’s students. I regularly teach calculus, linear algebra, real analysis, and senior seminar classes.

Current and Past Courses Taught

List of Courses

2021 – Winter: Math 143-09, -12 (Calculus III)

2021 – Winter: Math 419-01 (Introduction to the History of Mathematics)

2020 - Fall: Math 459-01 (Senior Project Seminar)

2020 - Fall: Math 550-01 (Real Analysis)

2020 - Fall: Math 580-01 (Proofs Seminar)

2020 - Spring: Math 202-01 (Orientation to Math Major)

2020 - Spring: Math 414-01 (Introduction to Analysis III)

2020 - Winter: Math 413-01,-02 (Introduction to Analysis II)

2019 - Fall: Math 202-01 (Orientation to Math Major)

2019 - Fall: Math 412-01,-02 (Introduction to Analysis I)

2019 - Fall: Math 580-01 (Proofs Seminar)

2019 - Spring: Math and Hnrs 241-70,-71(Honors Calculus IV)

2019 - Spring: Math 406-01 (Linear Algebra III)

2019 - Winter: Math and Hnrs 143-70,-71(Honors Calculus III)

2019 - Winter: Math 306-01 (Linear Algebra II)

2018 - Fall: Math and Hnrs 142-70,-71(Honors Calculus II)

2018 - Fall: Math 306-01 (Linear Algebra II)

2018 - Spring: Math and Hnrs 241-70,-71(Honors Calculus IV)

2018 - Winter: Math and Hnrs 143-70,-71(Honors Calculus III)

2018 - Winter: Math 344-03 (Linear Analysis II)

2017 - Fall: Math and Hnrs 142-70,-71(Honors Calculus II)

2017 - Fall: Math 459-01 (Senior Project Seminar)

2017 - Spring: Math 206-03 (Linear Algebra I)

2017 - Spring: Math 304-03,-04 (Vector Analysis)

2017 - Winter: Math 142-10,-12(Calculus II)

2017 - Winter: Math 412-01 (Introduction to Analysis I)

2016 - Fall: Math 143-17 (Calculus III)

2016 - Fall: Math 459-01, -02 (Senior Project Seminar)

2016 - Spring: Math 241-11,-13 (Calculus IV)

2016 - Winter: Math 143-05,-06 (Calculus III)

2016 - Winter: Math 419-01 (Introduction to the History of Mathematics)

2015 - Fall: Math 142-08 (Calculus II)

2015 - Fall: Math 344-04, -05 (Linear Analysis II)

2015 - Spring: Math 142-04,-05 (Calculus II)

2015 - Spring: Math 306-02 (Linear Algebra II)

2015 - Winter: Math 244-03,-04 (Linear Analysis I)

2015 - Winter: Math 412-01 (Introduction to Analysis I)

2014 - Fall: Sabbatical Leave

2014 - Spring: Math 241-06 (Calculus IV)

2014 - Spring: Math 304-01,-02 (Vector Analysis)

2014 - Winter: Math 143-09,-13 (Calculus III)

2014 - Winter: Math 206-01 (Linear Algebra I)

2013 - Fall: Math 244-09, -11 (Linear Analysis I)

2013 - Fall: Math 550-01 (Real Analysis)

2013 - Summer: Math 143-01 (Calculus III)

2013 - Summer: Math 244-01 (Linear Analysis I)

2013 - Spring: Math 141-03 (Calculus I)

2013 - Spring: Math and Hnrs 241-70,-71(Honors Calculus IV)

2013 - Winter: Math and Hnrs 143-70,-71(Honors Calculus III)

2013 - Winter: Math 409-01 (Complex Analysis II)

2012 - Fall: Math and Hnrs 142-70,-71(Honors Calculus II)

2012 - Fall: Math 408-01 (Complex Analysis I)

2012 - Spring: Math 406-01 (Linear Algebra III)

2012 - Winter: Math 306-01, -02 (Linear Algebra II)

2012 - Winter: Math 419-01 (Introduction to the History of Mathematics)

2011 - Fall: Math 142-02,-03 (Calculus II)

2011 - Fall: Math 306-01 (Linear Algebra II)

2011 - Spring: Math 244-02, -03 (Linear Analysis I)

2011 - Winter: Math and Hnrs 241-70 (Honors Calculus IV)

2011 - Winter Math 241-05 (Calculus IV)

2011 - Winter Math 304-01 (Vector Analysis)

2010 - Fall: Math 202-01 (Orientation to Math Major)

2010 - Fall: Math and Hnrs 143-70 (Honors Calculus III)

2010 - Fall: Math 143-11 (Calculus III)

2010 - Fall: Math 550-02 (Real Analysis)

2010 - Spring: Math 241-07 (Calculus IV)

2010 - Spring: Math 414-01 (Introduction to Analysis III)

2010 - Winter: Math 142-14,17 (Calculus II)

2010 - Winter: Math 413-01 (Introduction to Analysis II)

2009 - Fall: Math 142-11 (Calculus II)

2009 - Fall: Math 202-01 (Orientation to Math Major)

2009 - Fall: Math 412-01,-02 (Introduction to Analysis I)

2009 - Spring: Math and Hnrs 241-70,-71(Honors Calculus IV)

2009 - Winter: Math and Hnrs 143-70,-71(Honors Calculus III)

2009 - Winter: Math 419-01 (Introduction to the History of Mathematics)

2008 - Fall: Math and Hnrs 142-70,-71(Honors Calculus II)

2008 - Fall: Math 202-01 (Orientation to Math Major)

2008 - Fall: Math 244-08 (Linear Analysis I)

2008 - Spring: Math 241-02, -04 (Calculus IV)

2008 - Winter: Math 143-05,-08 (Calculus III)

2008 - Winter: Math 419-01 (Introduction to the History of Mathematics)

2007 - Fall: Math 142-03, -08 (Calculus II)

2007 - Fall: Math 550-01 (Real Analysis)

2007 - Spring: Math 241-01, -03 (Calculus IV)

2007 - Winter: Math 143-04 (Calculus III)

2007 - Winter: Math 406-01 (Linear Algebra III)

2006 - Fall: Math 142-03 (Calculus II)

2006 - Fall: Math 306-01 (Linear Algebra II)

2006 - Spring: Math 482 (Abstract Algebra II)

2006 - Winter: Math 143-01,-03 (Calculus III)

2006 - Winter: Math 419-01 (Introduction to the History of Mathematics)

2005 - Fall: Math 142-01, -08 (Calculus II)

2005 - Fall: Math 459-01 (Senior Seminar)

2005- Spring: Sabbatical Leave

2005 - Winter: Sabbatical Leave

2004 - Fall: Math 143-01 (Calculus III)

2004 - Fall: Math 459-01 (Senior Seminar)

2004 - Spring: Math 143-01, -03 (Calculus III)

2004 - Winter: Math 143-06 (Calculus III)

2004 - Winter : Math 409-01 (Complex Analysis II)

2003 - Fall: Math 241-02, -04 (Calculus IV)

2003 - Fall: Math 408-01 (Complex Analysis I)

2003- Spring: Math 202-01 (Orientation to Math Major)

2003 - Spring: Math 406-02, 03 (Linear Algebra III)

2003 - Winter: Math 306-02, 03 (Linear Algebra II)

2002 - Fall: Math 202-01 (Orientation to Math Major)

2002 - Fall: Math 206-01, -02 (Linear Algebra I)

2002 - Spring: Math 143-11, -13 (Calculus III)

2002 - Spring: Math 202-01 (Orientation to Math Major)

2002 - Winter: Math 242-09, -10 (Differential Equations)

2001 - Fall: Math 143-02 (Calculus III)

2001 - Fall: Math 202-01 (Orientation to Math Major)

2001 - Fall: Math 241-05, -06 (Calculus IV)

2001 - Spring: Math 142-03, -08 (Calculus II)

2001 - Spring: Math 202-01 (Orientation to Math Major)

2001 - Winter: Math 482-01 (Abstract Algebra II)

2000 - Fall: Math 141-21 (Calculus I)

2000 - Fall: Math and Hnrs 141-70 (Honors Calculus I)

2000 - Fall: Math 202-01 (Orientation to Math Major)

2000 - Fall: Math 481-01 (Abstract Algebra I)

2000 - Summer: Math 116-01 (Precalculus Algebra I)

2000 - Summer: Math 117-01 (Precalculus Algebra II)

2000 - Spring: Math 241-05,-06 (Calculus IV)

2000 - Spring: Math 414-01 (Introduction to Analysis III)

2000 - Winter: Math 317-01, -02 (Topics in Engineering Mathematics)

2000 - Winter: Math 413-01 (Introduction to Analysis II)

1999 - Fall: Math 242-06, -07 (Differential Equations)

1999 - Fall: Math 412-01 (Introduction to Analysis I)

1999 - Spring: Math 241-07, -08 (Calculus IV)

1999 - Spring: Math 522-01 (Applied Analysis III)

1999 - Winter: Math 143-08, -09 (Calculus III)

1999 - Winter: Math 521-01 (Applied Analysis II)

1998 - Fall: Math 142-10, -11 (Calculus II)

1998 - Fall: Math 520-01 (Applied Analysis I)

1998 - Summer: Math 124-01 (Finite Mathematics)

1998 - Spring: Math 142-06 (Calculus II)

1998 - Spring: Math 206-01, -02 (Linear Algebra I)

1998 - Winter: Sabbatical Leave

1998 - Fall: Sabbatical Leave

1997 - Summer: Math 124-01 (Finite Mathematics)

1997 - Summer: Math 141-02 (Calculus I)

1997 - Spring: Math 116-06, -07 (Precalculus Algebra 1)

1997 - Spring: Math 119-01, -02 (Precalculus Trigonometry)

1997 - Winter: Math 141-03, -05 (Calculus I)

1997 - Winter: Math 409-01 (Complex Analysis)

1996 - Fall: Math 142-04, -09 (Calculus II)

1996 - Fall: Math 408-01 (Functions of a Complex Variable)

1996 - Spring: Math 104-05 (Intermediate Algebra)

1996 - Spring: Math 406-01 (Linear Algebra III)

1996 - Winter: Math 141-07 (Calculus I)

1996 - Winter: Math 306-01 (Linear Algebra II)

1996 - Winter: Math 550-01 (Real Analysis)

1995 - Fall: Math 141-09, -12 (Calculus I)

1995 - Fall: Math 206-01 (Linear Algebra I)

1995 - Spring: Math 141-01, -02 (Calculus I)

1995 - Winter: Math 142-03, 04 (Calculus II)

1995 - Winter: Math 502-01 (Methods in Applied Mathematics II)

1994 - Fall: Math 142-03, 06 (Calculus II)

1994 - Fall: Math 501-01 (Methods in Applied Mathematics I)

1994 - Spring: Math 414-01 (Advanced Calculus III)

1994 - Winter: Math 116-03, -04 (Precalculus Algebra I)

1994 - Winter: Math 413-01 (Advanced Calculus II)

1993 - Fall: Math 100-02 (Beginning Algebra Review)

1993 - Fall: Math 412-02 (Advanced Calculus I)

1993 - Spring: Math 141-01, -02 (Calculus I)

1993 - Winter: Math 241-02, -03 (Calculus IV)

1993 - Winter: Math 406-01 (Linear Algebra III)

1992 - Fall: Math 143-01, -02 (Calculus III)

1992 - Fall: Math 306-01 (Linear Algebra II)

1992 - Spring: Math 141-01, -02 (Calculus I)

1992 - Winter: Math 142-04, -10 (Calculus II)

1992 - Winter: Math 206-01 (Linear Algebra I)

1991- Fall: Math 143-03, -04 (Calculus III)

1991- Fall: Math 241-04 (Calculus IV)

1987-1990: Taught trigonometry and calculus at U.C. San Diego;

Taught Statistics, Calculus, and Survey of Mathematics at San Diego Mesa College.

Professional Distinctions

List of Distinctions

Invited talk: “A Composition Operator Norm Upper Bound on Multivariable Reproducing Kernel Hilbert Spaces”, American Mathematical Society Section Meeting, San Francisco, California, October 2018.

Invited talk: “Pick interpolation on the boundary of the bidisk”, Joint Mathematics Meetings, San Diego, California, January 2018.

Attended workshop: “Crouziex’s Conjecture”. American Institute of Mathematics, San Jose, CA. July 31-August 4, 2017.

Invited talk: “Numerical Ranges with Rotational Symmetry”, International Linear Algebra Society, Ames, Iowa, July 2017.

Flipped Classroom Workshop, Center for Teaching, Learning, and Technology, Cal Poly, August 2014.

SQuaRE workshop, ``Possible shapes of the numerical ranges for certain classes of matrices", American Institute of Mathematics, Palo Alto, May 2013.

Invited talk: ``Numerical Ranges of Some Block Toeplitz Composition Operators'', International Workshop on Operator Theory and its Applications, Sydney, Australia, July 2012.

Invited talk: ``Numerical Ranges of Some Cubic Operators'', Joint Mathematics Meetings, Boston, January 2012.

One of four Cal Poly faculty organizers for ``Cal Poly-San Luis Coastal Unified School District Mathematics Institute", San Luis Obispo, August 2011.

Group leader for ``Research Experience for Undergraduate Faculty" a workshop for faculty interested in undergraduate research, American Institute of Mathematics, Palo Alto, July 2011.

Presentation ``Non-Circular Numerical Ranges'', Southeastern Analysis Meeting, Gainesville, March 2011.

Invited talk: ``Introduction to Composition and Toeplitz Operators'', Hypatian Seminar, University of California, Santa Barbara, April 2010.

Workshop ``How to Start a Math Teachers' Circle" at American Institute of Mathematics, Palo Alto, July 2009.

Invited talk: ``Composition Operator Norm Inequalities'', American Mathematical Society meeting, Claremont McKenna College, May 2008.

Presentation ``Composition Operator Norm Inequalities'' at Classical Analysis Conference, University of North Carolina at Chapel Hill, September 2007.

Presentation ``Positive Definite Random Toeplitz Matrices'' at Robert C. Thompson Matrix Meeting, San Francisco State University, November 2005.

Workshop ``Teaching a Course in the History of Mathematics", MathFest, Albuquerque, August 2005.

Invited talk: ``The numerical range of a nilpotent n-tuple of operators," American Mathematical Society meeting, University of California, Santa Barbara, April 2005.

Presentation ``Pick Interpolation on the Boundary of the Bidisc'', International Workshop on Operator Theory and its Applications, Blacksburg, VA, August 2002.

Principal Investigator on $399,367 Computer Science, Engineering, and Mathematics Scholarships grant from the National Science Foundation, 2001-2004.

Presentation ``Extending Bounded Holomorphic Functions on the Polydisc'' at Southeastern Analysis Meeting, Charlottesville, VA, March 2000.

Invited talk: ``Representations of Holomorphic Functions on the Polydisc'' at the American Mathematical Society meeting in Gainesville, FL, March 1999.

Presentation ``Angular Derivatives and Nevanlinna-Pick Interpolation'' at Rocky Mountain Mathematics Consortium conference on composition operators at University of Wyoming, Laramie, July 1996.

Invited talk: ``Nevanlinna-Pick Interpolation on the Disc and Bidisc'' at University of California, Santa Barbara, March 1996.

Presentation ``Matrix Equations and Nevanlinna-Pick Interpolation'' at 5th annual meeting of the International Linear Algebra Society, at Georgia State University, Atlanta, August 1995.

Invited talk on ``Nevanlinna-Pick Interpolation '' at California State University, Sacramento, September 1994.

Invited talk on ``Nevanlinna-Pick Interpolation '' at California State University, Bakersfield, May 1994.

Presentation ``Boundary Interpolation on the Polydisc" at Southeastern Analysis Meeting (SEAM VIII) at

University of Tennessee, Knoxville, March 1992.

Cal Poly Mathematics Department Colloquia in 1992, 1994, 1999, 2001, 2005, 2008, 2012, 2018.

Sabbatical Leaves at University of California, Santa Barbara 1998 and 2005 and at Cal Poly, 2014.

Publications

List of Publications

(with S.L. Burnett and A. Chandler) Symmetric numerical ranges of four-by-four matrices. Involve 11:5 (2018) 803-826.

(with E. Militzer, I.M. Spitkovsky, M.C. Tsai) Numerical ranges of 4-by-4 nilpotent matrices: flat portions on the boundary. Operator Theory: Advances and Applications, Large truncated Toeplitz matrices, Toeplitz operators, and related topics 259 (2017) 561-591.

(with L. Deaett, R.H. Lafuente-Rodrigues, J. Marin Jr., K. Rasmussen, R.B. Johnson Yates) Trace conditions for symmetry of the numerical range. Electronic Journal of Linear Algebra 26 (2013) 591-603.

Some block Toeplitz composition operators. Journal of Mathematical Analysis and Applications 400:2 (2013) 363-376.

(with M. Mazzella, T.R. Harris, D. Renfrew, I. M. Spitkovsky) Numerical ranges of cube roots of the identity. Linear Algebra and its Applications 435 (2011) 2639-2657.

(with Hammond, C.) Norm inequalities for composition operators on Hardy and weighted Bergman spaces, Operator Theory: Advances and Applications 202 (2010) 265-272.

(with Robbins, M.) Approximating composition operator norms on the Dirichlet space. Journal of Mathematical Analysis and Applications 339:2 (2008) 1374-1385.

(with Putinar, M.) On multivariable Fejér inequalities. Acta Sci. Math. 72 (2006) 129-134.

(with Robbins, M.) Composition operators that are m-isometries. Houston Journal of Mathematics 31:1 (2005) 255-266.

(with Gu, C.) Commutation Relations for Toeplitz and Hankel matrices. SIAM Journal of Matrix Analysis and Applications 24:3 (2003) 728-746.

(with Eschmeier, J. and Putinar, M.) Caratheodory-Fejér interpolation on polydisks. Math Research Letters 7 (2000) 25-34.

Some solutions of the matrix equation for Nevanlinna-Pick interpolation. Linear Algebra and its Applications 254 (1997) 467-484.

Interpolation of Nevanlinna-Pick type on the boundary of the bisdisc. Complex Variables: Theory and Application 24: 1-2 (1994) 107-120.

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