20212022 Undergraduate Catalog [ARCHIVED CATALOG]
Mathematics and Computer Science


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Faculty
Mark E. Bollman, chair and professor.
B.A., Northwestern University; M.A., University of Michigan; Ph.D., Central Michigan University. Appointed 1999.
Paul L. Anderson, professor.
B.S., M.S., Ph.D., Colorado School of Mines. Appointed 1990.
Drew R. Ash, visiting assistant professor.
B.A., Ithaca College; M.S., Ph.D., University of Denver. Appointed 2017.
April Grow, visiting instructor of mathematics.
A.A. Grand Rapids Community College, B.S. Grand Valley State University, M.A. Central Michigan University. Appointed 2020.
Mauricio Marengoni, visiting assistant professor.
Ph.D., University of Massachusetts. Appointed 2021.
Darren E. Mason, professor.
B.S., Ph.D., University of Minnesota. Appointed 2001.
Karla R. McCavit, instructor and Director of the Quantitative Studies Center
B.S., Adrian College, M.S., Michigan State University. Appointed 1995.
David A. Reimann, professor.
B.S., University of Toledo; M.A., Ph.D., Wayne State University. Appointed 1996.
Yuming Zhang, assistant professor of computer science.
B.S., Tsinghua University. M.S., Institute of Electrical Engineering, China Academy of Science. Ph.D., University of New Mexico. Appointed 2020.
Introduction
The Mathematics and Computer Science Department at Albion College includes the disciplines of pure and applied mathematics, computer science and statistics.
The courses are structured to meet the overlapping needs of students who fall in one or more of the following categories: (1) those who wish to develop their appreciation of the power and beauty of mathematics; (2) those who wish to explore the dynamic field of computer science; (3) those who intend to pursue graduate work in mathematics, computer science or other related fields; (4) those who will exploit the applications of mathematics in the natural sciences, social sciences and other areas of quantitative studies; and (5) those who plan to enter the teaching profession in mathematics or computer science.
Computer science is the youngest of the liberal arts. It shares with mathematics strong historical ties as well as underlying valuses of abstraction, rigor and elegance. Throughtout history, mathematics and its algorithms have been developed to help the human condition improve. In the 20th centruy the development of the digital computer dramatically and positively transformed the modern world. Apple, Google, airbags, pacemakers, and a host of instances of human innovation would be impossible without this aspect of science. During its vigorous growth as an academic discipline, computer science has worked to map this abstraction onto physical devices. Computer science students will address significant problems: finiteprecision arithmetic, limited storage capacity of data, and bounded processing capacity of a computer. They will devleop distinct methodologies: programming languages, data encoding and the analysis of the complexity of algorithms in terms of time and space requirements. And they will experiment with some results distinctive to computer science: the exisitence of the generalpurpose computer, serial and parallele processing, and modularity and layers of adstraction in both hardware and software. This deep understanding of computer science will engage the student in discerning the benefits and limitations of computers in society.
The studey of algorithms is the theme underlying all aspects of computer science. Computer science students will learn to define a problem and specify a stepby step solution at a level of detail and clarity unparalleled in any other discipline. They will also examine the practical issues of efficient storage, manipulation and retrieval of data.
Computer science interact naturally with many other disciplines. Students will have opportunities to explore the interconnections amoung artificial intelligence, psychology and philosophy; to become involved in the physics and engineering of circuit design; to employ biological models in their study of genetic algorithms and neural networks; and to see aspects of grammar and linguistics in thier study of programming languages.
The major in data science at Albion College provides students with a rigorous quantitative plan of study including upperdivision courses in both mathematics and computer science which lead to a solid understanding of the principles of data management, analysis, modeling, and forecasting. Data science is an interdisciplinary field that combines mathematics, statistics, and computer science in the serious study of large amounts of information, with the goal of making data and statistically sound decisions in realworld problems across the spectrum.
Career Opportunities
There has long been a demand in both industry and government for people with training in mathematics and statistics. The mathematics major who takes courses in computer science or statistics will enter an extremely favorable job market. There is also a need for secondary school teachers who are certified to teach mathematics or computer science. A major in mathematics provides a good foundation for further study in mathematics or for teaching on the secondary school level. With a degree in mathematics, it is also possible to gain admission to graduate school in other fields such as public policy, management and operations research.
Computer science students will enter a very favorable job market with opportunities in business, industry, government and private consulting. The study of fundamental principles of computer science and the strong mathematical component of this program fortify students with the lifelong learning skills essential for success in this rapidly changing field. Students with a mathematics major and a computer science minor will be prepared for graduate work in this or a related field.
Data science is one of the fastestgrowing career areas worldwide. Majors will enter a very favorable job market with opportunities in business, industry, government, and private consulting.
Special Features
The Mathematics and Computer Science Department annually awards approximately $30,000 in scholarships in honor of E. R. Sleight, a beloved mathematics professor who taught at Albion from 1908 to 1948. Prospective students with strong interests in mathematics are encouraged to contact the department to apply for these scholarships. Additional awards are made to outstanding upperclass students in mathematics and computer science.
Each year the Mathematics and Computer Science Department nominates five mathematics majors to membership in the Mathematical Association of America. The J. R. Lancaster Award is presented to the student who best exemplifies the liberally educated mathematics student. The E. R. Sleight Prize and the Ronald C. Fryxell Prize are awarded to the outstanding seniors in mathematics and computer science. Each summer several students receive stipends as Kresge Fellows and from other sources for independent research projects in the mathematical sciences. The Michigan Alpha chapter (established at Albion in 1937) of the mathematics honorary Kappa Mu Epsilon promotes mathematical lectures, films and social events. Students participate in the Michigan Autumn TakeHome Challenge, the Lower Michigan Mathematics Competition, and at the national level, in the William Lowell Putnam Competition and the Mathematical Contest in Modeling. Students are encouraged to attend and present papers at departmental colloquia and at regional conferences in undergraduate mathematics. Internships and the Oak Ridge Science Semester provide additional opportunities for intensive study in the mathematical sciences.
The Math/Stat Computing Laboratory is designed especially for students in mathematics, statistics and computer science courses. This computer laboratory features microcomputers running Windows and a laser printer for highresolution graphics and typesetting. Statistics students routinely analyze data with the Minitab statistical analysis program; graphing calculators and the Mathematica computer algebra system are integrated into precalculus, calculus and higherlevel mathematics courses. This lab is part of Albion’s campuswide computer network connecting faculty offices, classrooms, laboratories, public computer areas, printers, the library automation system and residence hall rooms. From computers on the network, students can access their files, run software on the campus network, interact with other computers, send email and browse the World Wide Web.
The E. R. Sleight Computing Laboratory contains a network of workstations dedicated for use by computer science students. These computers run individually or in parallel under the Linux operating system.
Departmental Policy on Advanced Placement Credit
Credit earned through the Advanced Placement (AP) exams in calculus, computer science, or statistics may be applied, as appropriate, toward any major or minor in the department. Students who earn a 4 or 5 on the Calculus AB exam, or the AB subscore of the Calculus BC exam, receive credit for MATH 141 . Students who earn a 4 on the Calculus BC exam receive credit for MATH 141 , and those who earn a 5 on this exam receive credit for both MATH 141 and MATH 143 . Students who earn a score of 4 or 5 on the Computer Science A or Computer Science AB exam will receive credit for CS 171 . Students who earn a 4 or 5 on the statistics exam will receive credit for MATH 109.
Student Learning Outcomes
Students who complete the Mathematics B.A. major will be able to:

Articulate core concepts in calculus, differential equations & linear algebra, and analysis & algebra.

Write and understand abstract mathematical proofs, including those of algebraic, analytical, numerical, and logical type.

Demonstrate competence applying mathematical/quantitative concepts and methods to the modeling of real world phenomena.

Effectively use at least one higher level programming language to algorithmically solve both theoretical and practical problems.
Students who complete the Mathematics, Actuarial emphasis B.A. major will be able to:

Explain and apply micro/macroeconomic concepts as well as financial accounting/management methodology to the analysis of contemporary financial models & problems.

Understand and employ calculusbased single and multivariate methods in probability and statistics, with a view towards successfully sitting for the SOA/CAS P/1 Exams.

Apply financial, mathematical, and probabilistic methods to the modeling and analysis of financial concepts including bonds, derivatives, arbitrage, hedging, and risk management, which prepares students to successfully sit for the IFM/3 Exam.

Effectively use a statistical programming language such as R to employ actuarial riskmanagement concepts such as data analysis, forecasting, and asset hedging.
Students who complete the Mathematics B.A. with Elementary or Secondary certification will be able to:

Articulate core concepts in calculus, differential equations & linear algebra, and analysis & algebra.

Write and understand abstract mathematical proofs, including those of algebraic, analytical, numerical, and logical type.

Demonstrate competence applying mathematical/quantitative concepts and methods to the modeling of real world phenomena.

Effectively use at least one higher level programming language to algorithmically solve both theoretical and practical problems.

Students will be able to complete requirements for eligibility for certification.
Students who complete the Mathematics minor will be able to:

Articulate core concepts in calculus, differential equations & linear algebra, and analysis or algebra.

Write and understand abstract mathematical proofs, including those of numerical, logical, and algebraic (or analytical) type.

Effectively use at least one higher level programming language to algorithmically solve both theoretical and practical problems.
Students who complete the Applied Mathematics minor will be able to:

Articulate core concepts in calculus, differential equations & linear algebra.

Apply mathematical concepts ranging from elementary algebra, single and multivariate calculus, linear algebra, and differential equations to effectively model realworld phenomena.

Effectively use at least one higher level programming language to algorithmically solve both theoretical and practical problems.
Students who complete the Mathematics minor, with Secondary Education Certification will be able to:

Articulate core concepts in calculus, differential equations & linear algebra, and analysis or algebra.

Write and understand abstract mathematical proofs, including those of algebraic, analytical, numerical, and logical type.

Effectively use at least one higher level programming language to algorithmically solve both theoretical and practical problems.

Students will be able to complete requirements for eligibility for certification.
Students who complete the Statistics minor will be able to:

Articulate core concepts in calculus, differential equations & linear algebra, and analysis or algebra.

Understand and employ calculusbased single and multivariate methods in probability and statistics.

Implement various statistical methods for data analysis, inference, and modeling/forecasting in realworld situations.
Students who complete the Computer Science B.A. major will be able to:

Apply computer science theory and software development fundamentals to produce computingbased solutions.

Analyze a complex computing problem and apply principles of computing and other relevant disciplines to identify solutions.

Design, implement, and evaluate computingbased solutions that meet requirements in the context of the program’s discipline.

Effectively communicate professional contexts in oral and written form.
Students who complete the Computer Science minor can will be able to:

Design, implement, and evaluate computingbased solutions that meet requirements in the context of the program’s discipline.
 Effectively communicate professional contexts in oral and written form.
Students who complete the Data Science major will be able to:

Use appropriate statistical techniques and predictive analytics on available data to deliver insights and discover new relations.

Visualize complex and variable data.

Collect and integrate different data source and provide them for further analysis.

Employ at least one programming language (e.g., Python, R) and multivariate statistical techniques – including linear and nonlinear multivariable regression – to forecast model trends.

Design and implement programs that use a database, including using techniques for searching for patterns in data

Recognize and use efficient data structures and algorithms to solve datadriven problems.

Design the logical and physical structure for effective data management according to data type, data model, and application.

Understand the concept of data ethics, including tradeoffs between individual privacy and security.

Determine, apply, and evaluate a broad range of data mining and machine learning tools with implementations to real data.
ProgramsMajor Computer Science, B.A.
 Data Science, B.A.
 Mathematics, Actuarial Mathematics Emphasis, B.A.
 Mathematics, B.A.
 Mathematics, Elementary Education Emphasis, B.A.
 Mathematics, Secondary Education Emphasis, B.A.
 Mathematics, with Elementary Education Certification, B.A.
 Mathematics, with Secondary Education Certification, B.A.
Minor
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