少女福利

George Ashline

You can find below some 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, and more.

Material for my classes.

  • Math for Teachers, MA-115.
  • Elementary Statistics, ST-120.
    • An
    • , created and maintained by Robin Lock of St. Lawrence University.
    • , created by Robin Lock
    • Data and Story Library —
    • Quantitative Environmental Learning Projects —
    • from CAUSEweb
    • for data mining by KD Nuggets
    • for Burlington, VT
    • , part of the CUWU Statistical Program at Illinois-Champaign-Urbana.
    • An
  • Calculus I, MA-150.
  • Calculus II, MA-160.
  • Calculus III, MA-211.
  • Linear Algebra, MA-213.
    • Information about Jim Hefferon’s book.
  • Number Theory, MA-214.
    • , , and Number Theory topics list and links
  • Probability and Statistics, MA-251.
  • History of Mathematics, MA-284.
    • , indexes, and reference sources available at Saint Michael’s.
    • 聽and periodicals at Saint Michael’s.
  • Complex Analysis, MA-315.
    • Explorations in Complex Analysis .
  • Mathematics Education Seminar, MA-381.
    • 痴别谤尘辞苍迟鈥檚 and .
    • CBMS .
    • .
    • of assessments for beginning teachers.
    • The , 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
  • Real Analysis I, MA-401
  • Real Analysis II, MA-403
    • Background information on Fourier series from
    • Introduction to Fourier transforms by
  • Junior/Senior Seminar, MA-410
  • Abstract Algebra, MA-406

Advising and Departmental information.

General Information
Registrar’s Website

Study Abroad

Math Majors
Mathematics Dept Website
Mathematics Alumni Spotlights

Education Majors
Education Dept. Website

Math Career Information





and
, with a variety of Mathematical career interviews

My papers.

Copies of any of these manuscripts are available upon request.

鈥溾�� (with Bret Findley, Barbara O鈥橠onovan, Mitchell Andrea, Dylan Wawruck), Journal of Chemical Education (2024). 101, 5, 2134-2140. https://doi.org/10.1021/acs.jchemed.3c01098.

鈥溾�� (with Bret Findley, Mitchell Andrea, Dylan Wawruck), PRIMUS (2023 online, 2024). 34:3. 268-283. https://doi.org/10.1080/10511970.2023.2282541.

鈥�,鈥� (with Patti Frazer Lock) Math Horizons, 30: 4, (Apr. 2023) 12-15. doi: 10.1080/10724117.2023.2168388.

鈥�,鈥� PRIMUS. 30(6): 651-658. (2020). doi: 10.1080/10511970.2019.1700574

鈥�,鈥� (with Ian Adelstein), The College Mathematics Journal. 50 (1): 28-35 (Jan. 2019). doi: 10.1080/07468342.2019.1557983

鈥�,鈥� PRIMUS. 27(6): 598-605. (2017) doi: 10.1080/10511970.2016.1234528

鈥�,鈥� 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.), , 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.

“” (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), , 23: 2, (Nov.-Dec. 2009), 8-10.

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

“,” (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鈥y 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鈥檚 College,” , 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:

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 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.”

at the University of Minnesota offers a repository for materials and projects relating to the computation and visualization of geometric structures. Links to are also available.

Created with funding through the NASA Dryden Flight Research Center in Edwards, California, are provided for K-12 teachers.

Launched in December of 1999, campaign is intended to involve parents in their children鈥檚 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.

George P贸lya鈥檚 problem solving tips in 鈥溾��.

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

Kenneth Monks at the University of Scranton provides a couple of versions of his chapter , 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 . Also, see his NSF-sponsored for ideas on effectively using technology to integrate fractals and chaos into the classroom.

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

(a web resource of Wolfram, the maker of the CAS Mathematica) contains information about fractals and links to pertinent topics and resources. Also, provides information on fractals and their creation using the CAS Maple V.

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

Robert Doerner’s 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 may also be of interest.

The journal 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 , created for IBM PCs and compatible computers.

Here are some interesting sites on the history of mathematics:

Some useful links for the History of Mathematics include:

  • Comprehensive at the University of St. Andrews in Scotland.
  • at the University of Tennessee at Knoxville.
  • David Joyce’s at Clark University.
  • at the University of Tennessee at Martin.
  • .
  • Jeff Miller’s information on various , , and .
  • The Clay Mathematics Institute’s , offering a historical context for each problem.

Here are some interesting sites on number theory:

  • maintained by Chris Caldwell at UTM. Contains good information on .
  • Also, can check out (the Great Internet Mersenne Prime Search).
  • Information on and Faber’s .
  • Information on .

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

  • Homepage of the .
  • Information on ( is a quantitative literacy course developed by the Chance team at Dartmouth College).
  • and the NGISC report on the .