Vita: Dr. Carol JVF Burns

Doctor of Arts in Mathematics, May 1994, Idaho State University, Pocatello
GPA: 4.0/4.0
Featured Speaker at the Conference for the Advancement of Mathematics Teaching (CAMT), 2015
My three talks (each is ‘60 morsels in 60 minutes’) are available on my website:
Recipient of the MathWest Teacher of the Year Award for grades 7–12, 2007. This award recognizes a teacher in Western Massachusetts for outstanding contributions to the advancement of mathematics education and training.
Recipient of the Leonhardt Teaching Chair, Miss Hall’s School, Pittsfield, MA, 2002
Recipient of the first DA Student of the Year Award for the School of Graduate Studies and Research, 1994
Master of Arts in Mathematics, May 1984, University of Oklahoma, Norman
GPA: 4.0/4.0
Bachelor of Science Magna Cum Laude in Civil Engineering, February 1981, University of Massachusetts, Amherst
Summer Research Scholarship, Princeton University, 1980
Valedictorian, Monument Mountain Regional High School, Great Barrington, MA, 1976

College Teaching
Instructor of Mathematics, Northern Arizona University (2011–2012)
I got married in September 2011, had a long-distance marriage (Flagstaff/Tucson) for the academic year, and moved to Tucson in May 2012.
High School Teaching and Department Leadership
Chair of the Mathematics Department, Lenox Memorial Middle and High School, Lenox, MA (2008–2009)
I left this job to pursue math-on-the-web full-time. (I also did some consulting work and online tutoring.)

Mathematics Department, Miss Hall’s School (1999–2008)
University Teaching Experience
I taught mathematics at the university level for most of the period from 1981–1999: first while a graduate student at the University of Oklahoma; thereafter at Idaho State University, where I completed my doctoral degree and held a position as an Adjunct Assistant Professor of Mathematics. I taught a wide variety of undergraduate courses (listed alphabetically):
- algebra (all levels)
- analytic geometry
- calculus I, II, III (for majors)
- developmental mathematics
- differential equations
- foundations (introduction to the rigors of mathematical proof for math majors)
- language of mathematics
- linear algebra
- mathematics for elementary school teachers
- probability and statistics
- trigonometry
Engineering Technician (1995–1996)
I left academia for one year to work as an engineering technician at American Microsystems, Inc. (Pocatello, Idaho) and help them with some mathematical modeling problems. While there, I developed and implemented a genetic algorithm for multivariate function modeling. Also, I compiled, formatted, edited and typeset the first AMI Design Manual, a collection of application notes on a variety of aspects of circuit design.
Programming and Technology
Experience with MathJax, JavaScript, HTML, CSS, TeX, JSXGraph, and much more. I’m an independent learner. To acquire a new skill, I find a good book and read it cover-to-cover. Along the way, I ‘give back’ to the publisher/author by submitting errata—I’m an excellent proofreader, with keen attention to detail.

One Mathematical Cat, Please! (1998)
Many people have trouble with mathematics: not necessarily because the ideas are difficult, but because they are being presented in a foreign language. This book takes the time to teach the structure of the mathematical language, while exploring ideas that are central to all of mathematics—ideas that require no computational skill beyond arithmetic with numbers like 1, 2, and 3.

The book is appropriate as a supplement to any math class, from junior high school through college-level. (165 pages)

This book was ‘filled out’ to a complete first course in algebra, available both on my website and as an offline course.
Detecting Hidden Periodicities in Discrete-Domain Data (1994)
This book is written for the person who has a data set (a collection of ordered pairs), and who seeks to understand this data, for the primary purpose of predicting future behavior of the process that generated the data.

The dissertation is written as the basis for a textbook, and assumes a mathematical background typical of an undergraduate degree in engineering. Implementation of all techniques is incorporated throughout the text, using the MATLAB software package. (321 pages)
Understanding Calculus (1993)
To fulfill a teaching internship requirement at Idaho State University, I wrote a calculus book (about 450 pages) that incorporates mathematical language issues, and taught from it. I also wrote a complete Solutions Manual and MATLAB supplement.
Survey of Undergraduate Mathematics (1991)
While preparing for an exam over all undergraduate mathematics, I compiled an extensive set of notes (about 300 pages) highlighting important ideas in all areas of undergraduate mathematics. These notes were still being used by DA students preparing for the written exam when I left ISU in 1999.

DR. CAROL JVF BURNS