Program Learning Outcomes
Last Revised: May 4, 2022
1. Departmental Student Learning Statement
The educational component of the mission of the Department of Mathematics and Statistics is to provide effective teaching in the mathematical sciences to the students of the University of Maine using competitive and intellectually challenging curricula.
We strive to give all students an appreciation both for the intrinsic beauty of Mathematics and for the significance of these subjects in relation to understanding the complexity found in our dynamic world.
We will periodically evaluate the efficacy of our educational efforts within each Mathematics degree program by measuring student performance against benchmarks set in each specific targeted learning outcome documented in Section 2 below.
1.1. Undergraduate Students
We contribute to the education of University of Maine undergraduates through imparting skills in logical reasoning and communication that are quantitative and analytic in nature. We provide mathematical training to three pools of undergraduate students.
- For all students, we offer general education courses that fulfill the quantitative literacy component of the University’s General Education Requirements. In these courses, students gain experience working with quantitative techniques, and develop an understanding of the role that quantitative thought plays in analyzing real world problems and relationships.
- For students majoring in STEM areas outside of mathematics, we provide the fundamental mathematical tools and knowledge that will serve them to progress in their fields of study.
- For majors in mathematics, we offer a robust program of study that teaches the importance of rigorous logical argument and exposes students to a wide range of quantitative methods and tools for problem-solving that will support any kind of future professional activity.
1.2. Graduate Students
We contribute to the Learning Goals of the University of Maine Graduate School by developing engaged scholars and professionals who will be prepared to contribute meaningfully to the advancement of the state of Maine, the nation and the global community. To these University of Maine students we impart skills in logical reasoning and communication that are quantitative and analytic in nature.
We provide mathematical training to two pools of graduate students.
- For graduate and advanced undergraduate students in STEM areas outside of mathematics, our graduate-level courses provide the advanced mathematical tools and knowledge that will serve them to progress in their fields of study.
- For master’s students in mathematics, we offer a robust program of study that teaches the importance of rigorous logical argument, and exposes students to a wide range of advanced quantitative methods and tools for problem-solving that will support any kind of future professional activity.
2. Mathematics Learning Goals and Outcomes
The department currently offers a Bachelor of Arts in Mathematics (BA), a Bachelor of Science in Mathematics (BS), and a Master of Arts in Mathematics (MA). What follows are the minimal Program Learning Outcomes (PLOs) anticipated for these programs. Many students will surpass these.
2.1. Bachelor of Arts in Mathematics (BA)
Learning Goals: A student in the Mathematics BA program gains a general appreciation of mathematics and mathematical proof, knowledge of mathematical theory, the ability to make rigorous logical arguments, experience with applications, recognition of connections between different branches of mathematics, the ability to communicate technical ideas, and the ability to work independently on a mathematical problem.
Program Learning Outcomes: Upon completion of a Mathematics BA, students will be able to:
BA1. Apply critical reasoning to analyze a written mathematical proof, with the ability to locate and correct logical fallacies; construct a logical argument in the form of a mathematical proof.
BA2. Explore an open-ended problem, either real-world or abstract, gain insight by applying an appropriate mathematical framework and effectively report the results.
BA3. Synthesize new material from non-specialist, peer-reviewed mathematics as can be found in periodicals such as American Mathematical Monthly, Mathematical Intelligencer, or SIAM News and communicate findings to technical and non-technical audiences.
2.2. Bachelor of Science in Mathematics (BS)
Learning Goals: In addition to the learning goals of the Mathematics BA program, students in the Mathematics BS program will attain greater depth in the mathematical sciences as is compatible with a stronger focus on the natural, computational, and/or engineering sciences. With additional required mathematics credits compared to the Mathematics BA, students in the Mathematics BS program will gain knowledge in additional branches of mathematics, and further their understanding within the core areas of mathematics. Consequently, the Mathematics BS program will offer a stronger preparation for graduate study in mathematics than the Mathematics BA.
Program Learning Outcomes: Upon completion of a Mathematics BS, students will attain each of the learning outcomes given above for the Mathematics BA and in addition be able to:
BS4. Demonstrate knowledge in a broad set of mathematical core areas, including mastery of either real analysis or abstract algebra at a level as taught in a two-semester course sequence in these areas.
Note that this document only lists the Program Learning Outcomes. Documentation on the Department’s Program Assessment Plan is available on request.
2.3. Master of Arts in Mathematics (MA)
Program Learning Outcomes: Upon completion of an MA in mathematics, students will be able to:
MA1. Develop approaches to abstract or real-world problems by drawing upon knowledge of core areas of advanced mathematics, including linear algebra and real analysis. (GSLG 1, 3)
MA2. Demonstrate a professional facility with proof writing. (GSLG 1, 2, 3)
MA3. Research an advanced mathematical problem and present the findings clearly and convincingly to mathematical peers. (GSLG 1, 2, 3)