### Math Consultants for Fall 2022

September 2nd 2022

September 2nd 2022

April 11th 2022

The Frederick and Marion Steen Mathematics Scholarship was established in honor of Frederick and Marion Steen by their children.

This prestigious, merit-based scholarship is awarded annually to a full-time student in their third year majoring at Allegheny College in the natural sciences. The purpose of this fund is to partially cover senior year tuition expenses for one selected student per year.

According to the terms of the Scholarship, “the recipient should demonstrate the following character:

- strong understanding of and skills in the application of the principles of mathematics
- ability to communicate and enthuse others with the beauty of mathematics
- commitment to put mathematics to purpose in a teaching, engineering, or scientific profession.”

A natural sciences major who anticipates graduating in 2023 and wishes to be considered for this scholarship should submit their application via email to Professor Ellers (hellers@allegheny.edu), the Chair of the Mathematics Department. Applications should contain the following:

- a letter of interest that addresses the three criteria listed above, and
- a pdf copy of your transcript. (Unofficial is OK.)

**The deadline for completed applications is April 24, 2022. **Applications will be reviewed by the Mathematics department faculty shortly thereafter.

March 25th 2022

Charles A. (Chuck) Cable, a mathematics educator and Professor Emeritus from Allegheny College, Meadville, Pennsylvania, died on September 16, 2021 following a 24 year battle with prostate cancer. He was born on January 15, 1932 in Akeley, PA and is a son of Elton and Margaret (Fox) Cable. In 1955 he married Mabel E. Yeck.

Chuck graduated from Edinboro University of Pennsylvania in 1954 with a BS Degree in mathematics and he began teaching high school mathematics and physics in Interlaken, New York in the fall of 1954. His teaching was interrupted in January of 1955 when he was drafted into the U.S. Army where he served for two years at Fort Chaffee, Arkansas. After being honorably discharged in January 1957, Chuck taught at Tidioute High School in Tidioute, PA. He enjoyed teaching mathematics there for 1½ years. At this point he needed to obtain more college credits to become a permanently certified teacher in the State of Pennsylvania. Normally the GI Bill would have provided the tuition for these credits but the GI Bill had ended in 1956 and was not reinstated until 1968. Scholarships were being offered by National Science Foundation (NSF) and also General Electric (GE) and he applied. Chuck was surprised when he received two telegrams announcing that he was awarded both the 1958 Summer GE Fellowship at Rensselaer Polytechnic Institute and a full year NSF at the University of North Carolina (UNC) starting in the fall of 1958. He earned a M.Ed. degree in mathematics from UNC in 1959 and then held a position as Assistant Professor of Mathematics at Juniata College in Huntingdon, PA from 1959 until 1967.

At the beginning of a long but important journey in his life he attended the NSF Summer Fellowship at Bowdoin College in Brunswick, ME in 1962. Upon returning to Juniata College in the fall of 1962 he continued to enjoy teaching full time while attending evening classes at Penn State University. He received another NSF Summer Fellowship in 1964 and while on sabbatical leave in 1965 he passed the written exams for the Ph.D. After receiving a one year NSF Faculty Fellowship in 1967 and a National Defense Act Fellowship in 1968 he graduated from Penn State University with a Ph.D. in mathematics in 1969. His Ph.D. dissertation was titled “The Decomposition of Certain Group Rings” and was written under the supervision of Dr. Raymond Ayoub. In 1969 Chuck was appointed as an Associate Professor of Mathematics at Allegheny College in Meadville, PA. He was promoted to the rank of Full Professor in 1975.

Shortly after starting at Allegheny College Chuck became chair of a young math department with the goal of making it one of the best in the college. He skillfully and successfully led the department for 20 years. He was especially proud of his efforts to institute a Math Department Speakers Series in 1972 which invited nationally known mathematicians to give a week-long series of talks at Allegheny College each Fall Term and Spring Term. These speakers also interacted with students in small group discussions and at mealtimes both on campus and at the Cable home. He also began an annual publication of Math News which was distributed to all Math Alumni of the College.

Chuck was held in high esteem by his colleagues on the faculty of Allegheny College. He was elected to serve five three year terms on Faculty Council. He served as Chair of the Science Division and a two year term as President of the local Chapter of the American Association of University Professors.

Dr. Cable was a member of the Mathematics Association of America (MAA) for sixty years at both the sectional and national level. He was Chairman of the Allegheny Mountain Section from 1973 to 1975. He instituted a session for undergraduate students to present research talks at the annual Allegheny Mountain Section Meeting. The Allegheny Section was the first section to have student sessions.

In 1982 Chuck was elected Governor of the Allegheny Mountain Section. The idea of instituting student chapters was strongly supported by Chuck and he worked hard to convince the other Governors of its value. The Student Chapter Program passed in 1984, the final year that he was a Governor. He served on the Committee for Student Chapters for the first six years of its existence. He is quoted in the February 2005 Focus saying, “When my initial efforts to form Student Chapters were unsuccessful, I was quite disappointed and I gave up. However, several months later Paul Halmos urged me to try again saying that sometimes it takes a while to get used to new ideas. I followed his suggestion and found that he was correct. The persistence eventually paid off.”

He took a sabbatical in 1986 spending a year at University of Colorado Denver where he joined a graph theory research group. He became involved in a project where he and his new colleagues introduced niche graphs, an extension of competition graphs which arose from the study of food webs. Fortuitously it was presented by a coauthor as part of a talk at a special workshop at the University of Minnesota on applications of graph theory to the biological and social sciences. As a result of this exposure and Chuck’s first paper in 1989, several mathematicians became interested in niche graphs and wrote a variety of papers. Working with various combinations of five coauthors, Chuck published seven papers on the topic from 1989 to 2001. A particularly nice paper was a complete characterization of niche graphs and mixed pair graphs of tournaments found by Chuck and his coauthors. Chuck retired in 1996, but he continued his graph theory research after the niche graph papers and published three papers on king sets and quasi-kernels from 2005 – 2012.

He was honored to serve as one of the first group of Associate Editors of the MAA’s Focus. His outstanding service to the Allegheny Mountain Section was recognized in 2003 with the Section Service Award. In January 2005 Chuck received a Meritorious Service Award in Mathematics from the MAA at a ceremony in Atlanta, GA for his service to the MAA at both the sectional and national levels.

Chuck enjoyed competing in various sports activities throughout his life. While he was a faculty member at Juniata College he played handball, basketball and tennis. During the years when he was a professor at Allegheny College he engaged in tennis, racket ball, sailing and downhill skiing. After he retired he continued downhill skiing, sailing and playing tennis. He was admired for his great sense of humor. Music played a very important part in his life. He played the trumpet for many years, sang in the Meadville, PA First Presbyterian Church Choir and in the barbershop chorus at the Green Mountain Presbyterian Church of Lakewood, CO.

In addition to his loving wife, Mabel, of 65 years, he is survived by two children, Christopher Cable and his wife Nancy of Dallas, TX and Carolyn Blinsmon and her husband Brad of Denver CO; three grandchildren Ryan Cable and his wife Isabel, Dr. Tracy Cable and her husband Barrett Davis, and Heather Blinsmon; one great grandchild David Cable. He is also survived by a twin brother Clair Cable and his wife Monchaya, who reside in Russell, PA and Bangkok, Thailand and a niece and three nephews. He was preceded in death by his parents.

Memorial contributions may be made to the Charles and Mabel Cable Fund for Visiting Scholars and Speakers in support of the Department of Mathematics at Allegheny College, Institutional Advancement, 520 Main Street, Meadville, PA 16335.

This obituary was written by his wife, Mabel E. Cable and his colleague, Dr. Richard Lundgren, Professor Emeritus, University of Colorado Denver

References:

- News Release, The Mathematical Association of America, Washington, D.C., January 6, 2005, Five Mathematicians Honored with Meritorious Service Awards.
- Joint Mathematics Meetings, Atlanta, GA, January 5-8, 2005, Program Booklet, Certificates of Meritorious Service, p.27-28.
- MAA Focus, Vol.25, No.2, February 2005. Fernando Gouvea and Joe Gallian, Prizes and Awards at the Atlanta Joint Mathematics Meetings, Section Certificates of Meritorious Service, Charles Cable, p.14.
- MAA Focus, Vol.4, No.61/November-December 1984, Charles Cable, U.S. Students Rank Below Students from Other Countries in International Study, p.1.
- MAA Focus, Vol.36. No. 6, December 2015/January 2016, Kenneth A. Ross, Interview: Aperna Higgens, p. 19-20.
- Personal Communication

March 30th 2021

The Frederick and Marion Steen Mathematics Scholarship was established in honor of Frederick and Marion Steen by their children.

This prestigious, merit-based scholarship is awarded annually to a full-time student in their junior year who is majoring at Allegheny College in the natural sciences and will partially cover senior year tuition expenses.

According to the terms of the Scholarship, “the recipient should demonstrate the following character:

- strong understanding of and skills in the application of the principles of mathematics
- ability to communicate and enthuse others with the beauty of mathematics
- commitment to put mathematics to purpose in a teaching, engineering, or scientific profession.”

A junior natural sciences major who wishes to be considered for this scholarship should submit their application by email to Professor Lakins (tlakins@allegheny.edu), Chair of the Mathematics Department. Applications should contain the following:

- A letter of interest that addresses the three criteria listed above, and
- A pdf copy of your WebAdvisor transcript.

**The deadline for completed applications is April 21, 2021. **Applications will be reviewed by the Mathematics department faculty shortly thereafter. Please contact Professor Lakins (tlakins@allegheny.edu) if you have questions.

October 26th 2020

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September 17th 2020

The Math department congratulates Math major and Economics minor Mica Hanish ’21, who was named NCAC Student-Athlete of the Week. As noted in the announcement:

Hanish, a mathematics major with a 4.00 cumulative GPA, was named a CoSIDA Academic All-America first-team selection last season, only the third individual in Allegheny women’s track & field and cross country history to earn that honor. She is also a distinguished Allegheny Alden Scholar (GPA above 3.80) and is a member of Chi Alpha Sigma, the national student-athlete honor society, and Pi Mu Epsilon, the national mathematics honor society, where she serves as treasurer of Allegheny’s chapter. In her cross country career, Hanish has garnered All-NCAC selections three times, including two first-team honors and one second-team honor, while also earning three All-Region honors. On the track, she has earned All-NCAC accolades in the 3000-meter run, DMR, one-mile and 5000-meter run. In March, she was named All-Region for her performances in the mile and 3,000-meter run.

August 10th 2020

Allegheny College Mathematics Professor Dr. Tamara Lakins has received the 2020 Meritorious Service Award from the Mathematical Association of America (MAA).

The Certificate of Meritorious Service, announced in a video ceremony in July, was presented for service at the national level or for service to a section of the Mathematical Association of America. There were five award recipients honored nationwide.

Lakins has been active in the Mathematical Association of America since arriving at Allegheny in 1995. During her first year at Allegheny, she participated in the national MAA professional development program for new Ph.D.s, called Project NExT (New Experiences in Teaching).

“Many aspects of Project NExT greatly informed my teaching as a new professor at Allegheny,” said Lakins. “My continued relationship with MAA’s Project NExT, both nationally and in the local Section NExT I helped cofound in 1999, has enabled me to stay connected with current pedagogical conversations. Participating, and eventually becoming a leader, in the local MAA section gave me a valuable connection to the local mathematics community in western Pennsylvania and West Virginia. I have greatly valued and benefited from those friendships and professional relationships, and I was greatly honored to receive a 2020 MAA Certificate of Meritorious Service.”

“The individuals we honor represent the spirit of community that is at the heart of the Mathematical Association of America,” said Michael Pearson, executive director of the MAA. “Their willingness to give of their time, energy, and expertise to benefit their Sections and beyond serves as a fresh reminder of why the MAA remains so close to my heart.”

The Mathematical Association of America is the world’s largest community of mathematicians, students and enthusiasts. Its mission is to accelerate the understanding of the world through mathematics because mathematics drives society and shapes lives. Learn more at maa.org.

May 11th 2020

The faculty and staff of the Mathematics department congratulate Math major Ryan Clydesdale and Math minor Olivia Krieger on being named co-valedictorians of the class of 2020. Ryan and Olivia, although we weren’t able to celebrate you in person this year, we are very proud of your achievements.

Ryan Clydesdale, a Math major with a double minor in Chemistry and Economics, was also awarded the Frederick H. Steen Prize for Excellence in Mathematics and was a previous recipient of a Cornerstone Research summer internship. A member of the men’s soccer team, Ryan also received the William Crawford Academic Merit Award in Athletics – Male, recognizing him as the male scholar-athlete with the highest grade-point average.

Olivia Krieger, a Physics major with a double minor in Mathematics and Philosophy, was also awarded the Richard L. Brown Physics Prize. Olivia presented her research at the 2019 Conference for Undergraduate Women in Physics, where she also won best poster in her category.

May 5th 2020

Will Crosby `21, Mica Hanish `21, and Megan Powell `21, students in Professor Tamara Lakins’ spring 2020 Mathematics Junior Seminar, chose the May 2020 winner of *The* *College Mathematics Journal Next Generation Prize*. The prize was awarded to the journal article in the May 2020 issue that the students selected as the best for undergraduate mathematics students nationwide to read. The prize was created to promote undergraduate students’ reading of *The College Mathematics Journal* (published by the Mathematical Association of America), and to encourage the writing of expository mathematics that is student-accessible. The Allegheny College students were thanked in the May 2020 issue.

April 2nd 2020

**MATH 205 – Foundations of Mathematics
**Instructor: Professor Lakins

An introduction to concepts encountered in the study of abstract mathematics. Topics covered include logic, mathematical proofs, set theory, relations, functions, mathematical induction, and introductory number theory. The concepts of injectivity, subjectivity, and inverses are discussed as well as elementary computational tools such as the Division Algorithm and Euclid’s algorithm for the greatest common divisor. Additional topics may include cardinality, combinatorics, graph theory, algebraic structure, the real number system, and concepts of mathematical analysis.

**MATH 211 – Vector Calculus and Several Variable Integration
**Instructor: Professor Carswell

A study of integration of functions of several variables, including the use of polar, cylindrical, and spherical coordinate systems; and vector calculus, including vector fields, line and surface integrals, and the theorems of Green and Stokes.

May not be taken for credit if a grade of C or better in MATH 210 has already been received.

**MATH 270 – Optimization and Approximation
**Instructor: Professor Ellers

A study of optimization of functions of one variable and of several variables, including the Extreme Value Theorem and Lagrange multipliers; sequences and series; and Taylor approximation of functions.

May not be taken for credit if a grade of C or better in MATH 170 has already been received.

**MATH 280 – Ordinary Differential Equations
**Instructor: Professor Carswell

An examination of methods of solving ordinary differential equations with emphasis on the existence and uniqueness of solutions of first order equations and second order linear equations. Topics may include Laplace transforms, systems of linear differential equations, power series solutions, successive approximations, linear differential equations, and oscillation theory with applications to chemistry and physics.

**MATH 325 – Algebraic Structures I
**Instructor: Professor Werner

An introduction to the notion of an algebraic structure concentrating on the simplest such structure, that of a group. Rings and fields are also discussed.

**MATH 340 – Introduction to Analysis
**Instructor: Professor Weir

An examination of the theory of calculus of a single variable. Topics include properties of the real numbers, topology of the real line, and a rigorous treatment of sequences, functions, limits, continuity, differentiation and integration.

Distribution Requirements: SP.

**MATH 345 – Probability and Statistical Inference I
**Instructor: Professor Lo Bello

A study of mathematical models, sample space probabilities, random variables, expectation, empirical and theoretical frequency distributions, moment generating functions, sampling theory, correlation and regression.

This is one of the possible mathematics courses that may be substituted for one of the required 300-level CMPSC courses in the Computer Science major.

**MATH 370 – Graph Theory and Combinatorics **New Course**
**Instructor: Professor Dodge

A study of finite graphs and combinatorics, covering enumeration of combinatorial structures, directed and undirected graphs, and recursive algorithms. Topics include trees, planarity, graph coloring, Eulerian and Hamiltonian graphs, shortest path algorithms, the pigeonhole principle, permutations and combinations of finite sets and multisets, binomial and multinomial coefficients, and the inclusion-exclusion principle.

This is one of the mathematics courses that may be substituted for one of the required 300-level CMPSC courses in the Computer Science major.