Our Programs

Mathematics, B.A

The Department of Mathematics and Statistics offers a Bachelor of Arts Degree in Mathematics. The program is designed to provide students with a broad background in mathematics and statistics. Students may, but are not required to, select one of four concentrations:

  • Applied Mathematics/Operations Research
  • Mathematics Education (grades 6-12)
  • Pure Mathematics
  • Statistics

Statistics, M.S.

The Department also offers a Master of Science degree in Statistics. Students select one of four concentrations:

  • Applied Statistics
  • Biostatistics
  • Data Science
  • Operations Research and Applied Mathematics.

Accelerated Graduate Pathway to the Statistics, M.S.

By carefully selecting the appropriate courses, one can complete both the Mathematics, B.A. and the Statistics, M.S. in five years. For general information about the Accelerated Graduate Pathway (AGP) in Statistics, review the AGP program page. For more detailed information, including prerequisites, grade requirements, and how to navigate the program, review the most current Undergraduate Catalog. The Statistics AGP information can be found by selecting Programs (A-Z) and then selecting Accelerated Graduate Pathways near the top of the page. Students interested in the Statistics AGP are encouraged to contact us.

Certificates

  • Actuarial Science (Undergraduate Certificate)
  • Applied Mathematics (Undergraduate Certificate)
  • Data Science (Undergraduate Certificate or Certificate of Graduate Study)
  • Mathematics (Undergraduate Certificate)
  • Statistics Undergraduate Certificate or Certificate of Graduate Study)

Undergraduate Minors

  • Actuarial Science
  • Applied Mathematics
  • Data Science
  • Mathematics
  • Statistics

Technology & Methodology

Students learn to use computer software packages such as Mathematica, MATLAB, Minitab, and SAS in their mathematics and statistics courses. Collaborative and active learning are encouraged throughout the curriculum.

Departmental Learning Outcomes:

  1. Graduate Study Preparation: Students are prepared for graduate studies in Mathematics (Pure or Applied) and/or Statistics.
  2. Teacher Education: Students wishing to do so are prepared to become teachers through the Secondary Teacher Education track.
  3. Professional Industry: Graduate students wishing to do so are prepared to work in industry.
  4. Core Concepts: Students will understand the core concepts in mathematics and to be able to successfully use what is learned in other courses at USM.
  5. Arguments and Proofs: Students will be able to construct logical arguments and proofs.
  6. Problem Solving: Students can demonstrate the ability to understand and solve mathematical and statistical problems.
  7. Information Evaluation: Students can demonstrate the ability to identify, evaluate, and apply different types of mathematical and statistical information to form judgements.
  8. Real-World Application: Students will be able to recognize how to solve real-world problems when related to mathematics, statistics, and other STEM-related fields.

Introductory-Level Course Learning Outcomes

  • Use the symbols and vocabulary of basic mathematics correctly.
  • Approximate solutions and identify solutions that do not make sense.
  • Use arithmetic skills of real numbers.
  • Translate mathematical and numerical information into verbal information, and vice versa.
  • Demonstrate mastery of basic algebraic skills.
    • Manipulate and evaluate algebraic expressions.
    • Utilize function notation.
    • Apply properties of exponents.
    • Write numbers using scientific notation.
    • Simplify and perform operations involving rational expressions.
    • Simplify square roots and estimate expressions involving radicals.
    • Solve linear equations.
    • Graph equations on a rectangular coordinate system.
    • Solve linear inequalities.
  • Demonstrate proficiency solving problems involving percent.
  • Solve problems using ratio and proportion, including converting from one unit of measurement to another using unit fractions.
  • Perform set operations of union, intersection, and complement.
  • Use prerequisite concepts and skills of the arithmetic of real numbers.
  • Manipulate and evaluate algebraic expressions.
  • Solve linear equations.
    • Apply linear equations to problems.
    • Write and graph linear equations on a rectangular coordinate system.
    • Use function notation and distinguish between input and output.
  • Perform operations involving polynomials.
    • Factor polynomials.
    • Solve polynomial and quadratic equations by factoring.
    • Apply rules of exponents and use scientific notation.
    • Simplify and perform operations involving rational expressions.
    • Solve equations containing rational expressions.
  • Simplify and perform operations involving radicals and rational exponents.
    • Solve equations involving radical expressions.
    • Solve quadratic equations by taking square roots, and by the quadratic formula.
    • Given a quadratic function, find its vertex and intercepts and graph the parabola.
  • Model and solve application problems.
  • Use the symbols and vocabulary of basic mathematics correctly.
  • Recognize the differences between inductive and deductive reasoning.
  • Correctly use numerical computation and to utilize appropriate technology.
  • Use algebraic models, and to identify the distinction between linear and exponential models.
  • Be able to organize and present data in appropriate and effective ways, using verbal and written methods, and using correct notation and symbols.
  • Analyze and interpret data using appropriate statistical tools and technological tools.
  • Identify the impact of compound interest and the effect of interest rates and length of term in financial decision making.
  • Compute simple probabilities and expected values and to explain how these concepts influence many aspects of our lives.
  • Simplify algebraic expressions using properties of real numbers, rules of exponents, and strategies for factoring.
  • Analyze and solve problems involving linear, quadratic, and absolute value equations and inequalities.
  • Solve radical, logarithmic and exponential equations.
  • Identify properties of functions, including domain, range, operations, compositions, and inverses.
  • Identify graphs of basic functions and use function operations to sketch the graph of new functions.
  • Express and discuss algebraic analysis in multiple ways: symbolically, numerically, graphically, verbally, and in writing.
  • Examine functions analytically and graphically, and to use them to construct and interpret models of real-world phenomena.
  • Describe a data set including both categorical and quantitative variables.
  • Apply laws of probability to concrete problems.
  • Compute probabilities related to the binomial, Poisson, and normal distributions.
  • Construct and interpret confidence intervals.
  • Perform hypothesis tests and clearly articulate the conclusion and type of error that might have been made.
  • Demonstrate competency in commonly utilized technology for statistical decision making.
  • Analyze data and develop a statistically based strategy to apply the results in a real world situation.
  • Recognize that data are numbers within a context. The result of any calculation involving data will be meaningful within the same context and have an appropriate label.
  • Recognize that the most common sources of numerical data are measurements in real-world situations.
  • Describe and interpret statistical situations using symbolic, verbal, and graphical representations.
  • Parse and evaluate logical statements and forms.
  • Assess logical arguments for validity.
  • Work with and perform operations on basic sets.
  • Work with functions within a modular space.
  • Understand and verify properties of relations and functions.
  • Prove or disprove statements and the countability of infinite sets.
  • Use counting methods to determine the number of elements in a list or set, size of large groups, and basic probabilities.
  • Know the definition of a limit and be able to determine limits using limit laws.
  • Understand the concept of continuity.
  • Find the derivative of a function using the definition.
  • Differentiate functions by rules such as the sum, product, quotient, and chain rules, as well as implicit differentiation.
  • Identify local and absolute extreme values of functions using the first and second derivative tests.
  • Sketch the graph of a function using techniques of calculus including the first and second derivative tests along with other tools such as asymptotes.
  • Compute Riemann sums and know the definition of the integral.
  • Understand the fundamental theorem of calculus and be able to evaluate integrals, including using the method of substitution.
  • Solve applied problems using techniques of calculus.
  • Know how to differentiate the inverse of a function and apply that process to transcendental functions such as exponential, logarithmic, and hyperbolic functions.
  • Identify indeterminate forms and use L’Hôpital’s rule when appropriate.
  • Demonstrate understanding of basic integration techniques such as the substitution rule, integration by parts, trigonometric substitution, partial fractions, and improper integrals.
  • Find limits of sequences.
  • Evaluate geometric series.
  • Demonstrate an understanding of the concept of convergence and divergence of a series by using techniques such as the direct comparison test, limit comparison test, integral test, ratio test, root test, n-th term test, and alternating series test.
  • Determine the radius and interval of convergence of a power series as well as being able to determine Taylor and Maclaurin series.