# George Ashline

You can find below some information about my current classes, information about other classes that I have taught, advising information, my papers, and ways to reach me. I have also compiled links in a number of areas in which I am interested, including mathematics education, fractal geometry and chaos theory, the history of mathematics, finite mathematics, photo links, and Saint Michael’s College.

**Material for my Fall 2021 classes.**

**Math for Teachers I MA-115.**- Class meets on MWF from 8:30 to 9:35 AM in STE 109.
- A previous course information sheet

**Calculus III, MA-211.**- Class meets on MWF from 9:45 to 10:50 AM in STE 109.
- A previous course information sheet.
- A previous Maple info sheet.

**Linear Algebra, MA-213.**- Class meets on MW from 3:15 to 4:50 PM in STE 109.
- A previous course information sheet.
- Information about Jim Hefferon’s linear algebra book.

**Material for other classes.**

**Elementary Statistics, MA-120.**- An extended t-table
- Data Surfing on the WWW, created and maintained by Robin Lock of St. Lawrence University.
- Sports Data Page, created by Robin Lock
- Data and Story Library — DASL
- Quantitative Environmental Learning Projects — QELP datasets
- Datasets and data sources from CAUSEweb
- Data sets for data mining by KD Nuggets
- US Census Bureau
- National Weather Service for Burlington, VT
- Correlation Guessing Game, part of the CUWU Statistical Program at Illinois-Champaign-Urbana.
- An extended t-table

**Calculus I, MA-150.**- A previous course information sheet.
- A previous Maple info sheet.

**Calculus II, MA-160.**- Class meets on MWF from 9:45 to 10:50 AM in STE 215, Th from 8:30 to 10:05 AM in McCarthy Theatre.
- A previous course information sheet.
- A previous Maple info sheet.

**Number Theory, MA-214.**- A previous course information sheet.
- MathForum, MathArchives, and Wikipedia Number Theory topics list and links

**Probability and Statistics, MA-251.**- Previous course information sheet.

**History of Mathematics, MA-284.**- A previous course information sheet.
- Links for pertinent databases, indexes, and reference sources available at Saint Michael’s.
- Links for mathematics journals and periodicals at Saint Michael’s.

**Complex Analysis, MA-315.**- A previous course information sheet.
- A resource list.
- Explorations in Complex Analysis information, including the ComplexTool java applet.

**Mathematics Education Seminar, MA-381.**- A previous course information sheet, library reserved texts, bibliography of references and resources, and sample secondary texts available for use in lesson preparation..
- Vermont’s Framework of Standards and Learning Opportunities and Subject Area Endorsements.
- CBMS MET document.
- NCTM and Principles and Standards for School Mathematics.
- Praxis Series of assessments for beginning teachers.
- Other useful Mathematics Education sites, including Math Archives and Math Forum.
- The Vermont Mathematics Initiative, a comprehensive and content-intensive professional development program for mathematics teachers designed to ensure high quality mathematics instruction and high levels of mathematics learning in elementary schools across the state of Vermont
- SMC Mathematics Education Professor Tim Whiteford’s mathematics education teaching and learning resource page.

**Real Analysis I, MA-401**- A previous course information sheet

**Real Analysis II, MA-403**- A previous course information sheet.
- Radical Approach to Real Analysis and Second Printing Corrections
- MathForum, MathArchives, and Wikipedia Real Analysis topics list and links
- Background information on Fourier series from MathWorld
- Introduction to Fourier transforms by MathWorld

**Junior/Senior Seminar, MA-410.**- A previous course information sheet.

**Advising and Departmental information.**

**General Information**

Registrar’s Website

KnightVision

SMC online catalog

Study Abroad

**Math Majors**

Mathematics Dept Website

Mathematics Alumni Spotlights

Why Study Mathematics?

Mathematics Fact Sheet

**Education Majors**

Education Dept. Website

**Math Career Information**

AMS Mathematics Careers Information

Employment Information for Mathematical Sciences (EIMS)

UNC Wilmington Mathematics Careers Information

BYU We Use Math site

Research Experiences for Undergraduates (REUs) Summer Programs

Actuarial Information

American Academy of Actuaries and Society of Actuaries (SOA)

Plus Magazine, with a variety of Mathematical career interviews

### My papers.

Copies of any of these manuscripts are available upon request.

“Leader Lessons Learned: Transition Advice and a Top Ten List from a Former Chair ,” *PRIMUS*. 30(6): 651-658. (2020). doi: 10.1080/10511970.2019.1700574

“Reframing the Pythagorean Theorem,” (with Ian Adelstein), *The College Mathematics Journal*. 50 (1): 28-35 (Jan. 2019). doi: 10.1080/07468342.2019.1557983

“Real-World Examples: Developing a Departmental Alumni Network,” *PRIMUS*. 27(6): 598-605. (2017) doi: 10.1080/10511970.2016.1234528

“Career Arcs and Advice: Voices from the Field,” *Math Horizons*, 23: 4, (Apr. 2016) 28-30.

“Vermont Middle Level Mathematics Initiative: Courses and Materials for Mathematics Educators,” (with Marny Frantz), In C. Beaver, L. Burton, M. Fung, and K. Kruczek (Eds.), Resources for Preparing Middle School Mathematics Teachers, MAA Notes, Volume 80, MAA: Washington, DC (2013) 169-179.

“Closing the Achievement Gap: Systemic Collaboration for Equity in Mathematics,”(with Marny Frantz, Kendra Gorton, Sandy Hepp, and Stephanie Ratmeyer), In J. Bay-Williams and W. Speer (Eds.), Professional Collaborations in Mathematics Teaching and Learning: Seeking Success for All, NCTM 74th Yearbook, NCTM: Reston, VA (2012) 31-45.

“Multiple Ways to Solve Proportional Reasoning Problems” (with Leslie Ercole and Marny Frantz), Mathematics Teaching in the Middle School, 16:8, (April 2011), 482-490.

“Math and Bio 2010” (with Joanna Ellis-Monaghan, Zsuzsanna Kadas, and Declan McCabe). MAA FOCUS centerfold poster and accompanying article, 30: 3, (Jun.-Jul. 2010), 15-17.

“Modeling Seashell Morphology” (with Joanna Ellis-Monaghan, Zsuzsanna Kadas, and Declan McCabe). In UMAP/ILAP Modules 2009: Tools for Teaching (UMAP Modules in Undergraduate Mathematics and Its Applications, Bedford, MA: COMAP), Module 801, (2009) 101-139.

“Proportional Reasoning and Probability: A Professional Development Context for Mathematics Educators” (with Marny Frantz), Connect: Innovations in K-8 Science, Math, and Technology, 23: 2, (Nov.-Dec. 2009), 8-10.

“Using Checklists in Project Assessment,” MAA FOCUS, “Teaching Time Savers” article, 29: 5, (Oct.-Nov. 2009), 13.

“Using Mathematically-Rich Tasks to Deepen the Pedagogical Content Knowledge of Primary Teachers,” (with Regina Quinn), In B. Clarke, B. Grevholm and R. Millman (Eds.), Tasks in Primary Mathematics Teacher Education: Purpose, Use and Exemplars, Mathematics Teacher Education, Springer Science+Business Media LLC, 4 (2009) 197-214.

“What We Learned…By Organizing and Hosting an MAA Sectional Meeting,” (with Karl-Dieter Crisman, Jo Ellis-Monaghan, Zsu Kadas, Greta Pangborn, and Lloyd Simons) MAA FOCUS, 29: 3, (Apr./May 2009) 16-18

“Alumni Profiles of Saint Michael’s College,” Math Horizons, XV: 4, (Apr. 2008) 28-29.

“How High? How Long? How Fast? Modeling with Water Rockets and Calculus,” With J. Ellis-Monaghan, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, XVI: 2, (Jun. 2006) 121 – 137.

“Integrating Exit Questions into Instruction,” NCTM News Bulletin, 42, 3 (Oct. 2005) 6.

“A House of Your Own: The Mathematics of the American Dream (Part 2),” With J. Ellis-Monaghan, The New Jersey Mathematics Teacher, 63: 2, (May 2005) 20-26.

“Credit Cards and Cars: The Mathematics of the American Dream (Part 1),” With J. Ellis-Monaghan, The New Jersey Mathematics Teacher, 63: 1, (January 2005) 16-23.

“The Lottery: A Dream Come True or a Tax on People Who are Bad at Math,” With J. Ellis-Monaghan, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, XIV: 4, (December 2004) 303 – 314 .

“Water Rockets in Flight: Calculus in Action,” (with J. Ellis-Monaghan and A. Brizard), UMAP/ILAP Modules 2002-2003: Tools for Teaching, pp. 151-188. Interdisciplinary Lively Applications Projects are designed to motivate mathematical concepts and skills in the context of a practical application in another field.

“Home Sweet Home: A Financial Incentive for the Lower Level Mathematics Course,” with Jo Ellis-Monaghan. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, XI: 1, (March 2001) 16-26.

“Microcosm to Macrocosm: Population Models in Biology and Demography,” With Jo Ellis-Monaghan, Tools For Teaching 1999, 39- 80, UMAP unit 777.

“The Defect Relation for Meromorphic Maps on Parabolic Manifolds,” Memoirs of the American Mathematical Society, 139, 165, May 1999. Abstract (postscript file).

“How Many People are in Your Future? Elementary Models of Population Growth,” With Jo Ellis-Monaghan, Updated version republished in Kuntz, S., et. al., “Case Studies in Ecology.” New York: WCB McGraw-Hill, (1999). Also published in Making Meaning: Integrating Science through the Case Study Approach to Teaching and Learning, a compilation of case studies published by McGraw-Hill Primis. 42- 80 (1999).

“Interdisciplinary Population Projects in a First Semester Calculus Course,” With Jo Ellis-Monaghan, PRIMUS, IX, 39-55, March 1999.

### Here are some interesting sites on mathematics education:

Through the NCTM, a number of resources are available, such as the electronic version of Principles and Standards of School Mathematics.

The Math Forum is an online “Math Education Community Center” with links to Web resources, teaching materials, online discussion groups with other teachers, problems of the week (for grades 3-12), Ask Dr. Math (for math questions), and Teacher2Teacher (for teaching questions). You can browse and/or search K-12 lesson plans according to topic or grade level.

Math Archives offers online teaching materials and links, with such focal areas as Calculus Resources On-line, Graphing Calculators, JAVA and Other Interactive WWW Pages, Lessons, Tutorials, and Lecture Notes, Sites with K-12 Teaching Materials in Mathematics, and Visual Calculus. At its K-12 Teaching Materials, information can be obtained about Lesson Plans, Software, Topics in Mathematics, Contests and Competitions, and other topics of interest. At its Topics in Mathematics, useful information is accessible in such areas as Arithmetic, Algebra, Geometry, Trigonometry, Pre-calculus, Calculus, Statistics, and other areas.

Math Central is “a service for people involved in mathematics education from kindergarten to grade twelve”. It is “a meeting place for teachers to share resources, a service to teachers, students and parents who may need an answer to a mathematical question and a facility to allow teachers to carry on a dialogue amongst themselves” (through Teacher Talk).

The Eisenhower National Clearinghouse was created to “identify effective curriculum resources, create high-quality professional development materials, and disseminate useful information and products to improve K-12 mathematics and science teaching and learning.”

Coordinated by Scott Mandel, Teachers Helping Teachers is intended to is to provide some basic mathematics teaching tips, new ideas in methodologies, and a forum for sharing expertise with colleagues. Lesson plans and activities for mathematics teachers are also offered.

The Geometry Center at the University of Minnesota offers a repository for materials and projects relationg to the computation and visualization of geometric structures. Links to educational materials are also available.

Created with funding through the NASA Dryden Flight Research Center in Edwards, California, math activities based on NASA projects and aeronautical themes are provided for K-12 teachers.

Though the NSA’s Mathematics Education Partnership Program (MEPP) outreach program promoting mathematics and science education, learning units are available that were created through NSA-sponsored teacher workshops (Summer Institutes for Mathematics and Elementary Teachers).

Launched in December of 1999, Figure This – Math Challenges for Families campaign is intended to involve parents in their children’s education and help parents encourage their 10 to 14-year old children to do math problems together after school. Sample challenges and an index of the mathematics covered in the challenges can be obtained at the site . Also, there is a related Math is Power site.

Part of a research and development effort to deliver a full range of information resources to educators and students by the University of Kansas, the Explorer offers browsable and searchable curricular materials in mathematics.

The Columbia Education Center provides lesson plans created by teachers for use in their own classrooms. Materials are offered for the elementary (K-5), intermediate (6-8), and high school (9-12) levels.

The home page for the University of British Columbia’s Electronic Games for Education in Math and Science or E-Gems, with links to several of their “current research projects”, in which they “focus on the human-computer interaction issues associated with learning in an electronic game environment.” One of their goals is to “engage learners (9-14) in conscious reflective exploration of math concepts” which can be integrated with other forms of education.

George Pólya’s problem solving tips in “How to Solve It”.

### Here are some interesting sites on fractal geometry and chaos theory:

As described in the last chapter of their text Fractals, Graphics, and Mathematics Education, Michael Frame and Benoit Mandelbrot have created a Panorama of Fractals and Their Uses. This is intended to be a detailed wordbook or lexicon that orders alphabetically a wide mixture of fractal uses for the classroom. Frame and Mandelbrot also provide information on their introductory course in fractal geometry at Yale University, including some details on possible fractal software.

Kenneth Monks at the University of Scranton provides a couple of versions of his chapter Fractal Themes at Every Level, as well as his fractal course software and some of his pertinent student papers.

Robert Devaney at Boston University offers an interactive version of his chapter on The Fractal Geometry of the Mandelbrot Set: Periods of the Bulbs. Also, see his NSF-sponsored Dynamical Systems and Technology Project for ideas on effectively using technology to integrate fractals and chaos into the classroom.

Cynthia Lanius at Rice University details a fractals unit for elementary and middle school students that “adults are free to enjoy”. The unit describes various fractal properties and involves creating and interpreting such figures as the Sierpinski triangle, Jurassic Park fractal, and Koch snowflake.

Florida Atlantic University and the Broward County School District offer Pattern Exploration: Integrating Math and Science for the Middle School, containing a rich collection of fractal geometry teacher enhancement materials created through a joint NSF grant.

Eric Weisstein’s World of Mathematics (a web resource of Wolfram, the maker of the CAS Mathematica) contains information about fractals and links to pertinent topics and resources. Also, Alexander Walz provides information on fractals and their creation using the CAS Maple V.

Mathematics Archives and the Math Forum both provide a variety of fractal information and links to other online resources.

The Maryland Chaos Group provides a Chaos Gallery with interesting fractal graphics, chaos animations, and links to pertinent mathematics.

Robert Doerner’s Interacting with Chaos deals with non-linear dynamics and chaos and discusses four sample systems, starting with the logistic map and ending with the driven damped pendulum.

Tom Stoppard’s Arcadia may also be of interest.

The journal FRACTALS publishes peer-reviewed work in the form of full-length research papers, short communications, reviews of both technical and pedagogical nature, and popular articles. The table of contents and paper abstracts for previous issues are accessible.

As suggested by a number of the contributors to the text, one particularly effective means to generate fractal graphics is through the freeware fractal generator Fractint, created for IBM PCs and compatible computers.

There are many pages that offer interesting facts about mathematics and mathematicians. For example, the following sites may be of interest:

Harvey Mudd College’s Fun Facts, an archive of interesting mathematical facts.

Steven Finch’s information on various mathematical constants.

Jeff Miller’s information on various mathematical symbols, mathematical words, and mathematicians on stamps.

Mark Woodard’s examples of mathematician quotes.

### Here are some interesting sites on the history of mathematics:

Some useful links for the History of Mathematics include:

- Comprehensive MacTutor History of Mathematics Archive at the University of St. Andrews in Scotland.
- Math Archives at the University of Tennessee at Knoxville.
- David Joyce’s History of Mathematics at Clark University.
- HMC Math Dept’s Searchable database for Mathematics Magazine and the College Mathematics Journal
- Prime pages at the University of Tennessee at Martin.
- Mark Woodard’s Mathematics Quotation Server at Furman University.
- Jeff Miller’s information on various mathematical symbols, mathematical words, and mathematicians on stamps.
- The Clay Mathematics Instititute’s Millenium problems, offering a historical context for each problem.
- Archive of the Historia Matematica listserve and discussion group, at which all traditional and scholarly aspects of the history of mathematics are considered.

### Here are some interesting sites on number theory:

- The Prime Pages maintained by Chris Caldwell at UTM. Contains good information on Mersenne primes.
- Also, can check out GIMPS (the Great Internet Mersenne Prime Search).
- Information on Goldbach’s Conjecture and Faber’s million dollar award.
- Information on Ruth-Aaron pairs.

### Here are some interesting sites on lotteries and using lotteries in liberal arts mathematics course:

- Homepage of the Vermont Lottery.
- Homepage of the New Hampshire Lottery.
- Information on Using Lotteries to Teach a Chance Course (Chance is a quantitative literacy course developed by the Chance team at Dartmouth College).
- National Gambling Impact Study Commission and the NGISC report on the State of Lotteries at the Turn of the Century.