Math Department

MAT 051 Topics in Mathematics Corequisite | MAT 051 Sample Syllabus
Corequisite: MAT 121 Topics in Mathematics
Credits: 2 (NOTE: This developmental course cannot be used to satisfy degree or certificate requirements)
The course covers various topics in developmental mathematics to support students enrolled in MAT 121. Students apply remedial mathematics topics such as fractions, decimals, percent, order of operations, scientific notation, exponential notation, and solving equations to strengthen comprehension of college level topics in MAT 121. This course requires co-enrollment with MAT 121.

MAT 052 Statistics Corequisite | MAT 052 Sample Syllabus
Corequisite: MAT 122 Statistics
Credits: 2 (NOTE: This developmental course cannot be used to satisfy degree or certificate requirements)
The course covers various topics in developmental mathematics to support students enrolled in MAT 122. Students apply remedial mathematics topics such as fractions, decimals, percent, proportion, scientific notation, coordinates, slope, graphing of linear equations, and mathematical phrasing just-in-time to strengthen comprehension of statistical concepts. This course requires co-enrollment with MAT 122.

MAT 095 Beginning Algebra | MAT 095 Sample Syllabus
Prerequisite: MAT 090 with a grade of C or higher; or appropriate placement score
Credits: 3 (NOTE: This developmental course cannot be used to satisfy degree or certificate requirements)
This course covers all basic operations of real numbers, linear and literal equations, graphing lines (using tables, x and y-intercepts), the arithmetic of polynomial expressions including properties of exponents, solving and graphing linear inequalities, perimeters and areas of basic figures, scientific notation and intrasystem metric conversions. Technology tools are utilized in this course.

MAT 097 College Algebra Corequisite | MAT 097 Sample Syllabus
Prerequisite: MAT 095 with a grade of C or higher; or QMAT placement score > 21
Credits: 2 (NOTE: This developmental course cannot be used to satisfy degree or certificate requirements)
This course covers various topics in developmental mathematics to support students enrolled in MAT 100. Students learn remedial mathematics topics such as factoring techniques, define and simplify radical expressions, graph linear equations using slope-intercept concepts, apply the use of the Pythagorean Theorem, and solve rational, quadratic, and literal equations to strengthen comprehension of college level topics in MAT 100. This course requires co-enrollment with MAT 100.

MAT 111 Math for Educators I | MAT 111 Sample Syllabus
Prerequisite: MAT 099 with a grade of C or higher; or appropriate placement score
Credits: 3 (NOTE: Restricted to General Studies - Elementary Education Transfer Option and ECE Program students)
This course focuses on the critical Mathematical concepts necessary for students who are pursuing the Elementary Education Transfer Option in the General Education-Associate in Arts degree program. Students construct and apply problem solving techniques to solve problems, apply arithmetical operations on integers, rational numbers and decimals, and develop an understanding of mathematical relationships using equations, draw conclusions based upon geometric pattern and interpret data. Students construct geometric patterns and graphical data into algebraic equations; construct a geometric or graphical model given an algebraic equation. Instructor modeling is an integral component of the course.

MAT 112 Math for Educators II | MAT 112 Sample Syllabus
Prerequisite: MAT 111
Credits: 3 (NOTE: Restricted to General Studies - Elementary Education Transfer Option and ECE Program students)
This course continues the comprehensive focus on the critical Mathematics concepts necessary for students who are pursuing and Early Childhood and/or General Studies Elementary Education degree. Students develop an understanding of the principles of Euclidean geometry and use them to prove theorems. In addition, students apply Euclidean geometry to analyze the characteristics and properties of two and three-dimensional shapes, coordinate geometry, and transformations. Fundamental principles of probability and statistics explored. Students develop a deep level of understanding of geometry, probability, and statistics in order to become successful elementary and middle school teachers. Instructor modeling is an integral component of the course.

MAT 103 Mathematics for Business | MAT 103 Sample Syllabus
Prerequisite: MAT 095 with a grade of C or higher; or appropriate placement
Credits: 3
This course introduces the mathematical processes and techniques currently used in the field of business and finance. Students use practical examples throughout to illustrate the relevance of analyzing and interpreting data in business and financial management. Students learn sound decision making skills that will aid them in fulfilling their roles as citizens, consumers, employees, employers, investors, and entrepreneurs. The course introduces business statistics and continues with business and financial topics including bank services, business and consumer loans, simple and compound interest, payroll taxes, risk management, the mathematics of buying, break-even and cost-volume-profit analysis, discounts, markups and markdowns, inventory control, stocks and bonds, annuities and sinking funds, depreciation, interpreting financial statements and financial analysis.

MAT 121 Topics in Mathematics | MAT 121 Sample Syllabus
Prerequisite: College level mathematics course or QMAT placement score > 21 or appropriate multiple measures placement or
Corequisite: MAT 051 Topics in Math Corequisite
Credits: 3
This course explores a variety of topics in contemporary mathematics These topics include problem solving and critical thinking, personal finance, numeration systems, set theory, counting principles and probability theory, and voting methods.

MAT 122 Statistics | MAT 122 Sample Syllabus
Prerequisite: College level mathematics course or QMAT placement score > 21 or
Corequisite: MAT 052 Statistics Corequisite
Credits: 3
This introductory statistics course covers descriptive statistics, probability, and inferential statistics. Statistical content includes sampling, graphical summaries of data, measures of center and variability, probability theory and distributions, standard and non-standard normal distributions, the Central Limit Theorem, confidence intervals, one-sample hypothesis tests, linear correlation and regression. Statistical technology is used.

MAT 147 Mathematics for Technicians I | MAT 147 Sample Syllabus
Prerequisite: MAT 095 with a grade of C or higher; or appropriate placement score
Credits: 4 (NOTE: Restricted to Applied Manufacturing Option (MPA), Electronics Engineering Technology- Mechatronics Option (EEMO), Manufacturing Technology (MP), Electronics Engineering Technology – Biomedical Instrumentation Option (EEBI), Electronics Engineering Technology – Photonics Option (EEPH), Energy Utility Technology Certificate – (EUTC))
This course covers applied mathematical concepts and methods: Content includes a review of basic concepts of arithmetic operations on scientific and engineering notation and algebra. Students are introduced to simple equations, functions and graphs, geometry, right triangles, vectors and oblique triangles. Students learn applications to systems of linear equations, matrices and determinants, ratio, proportion and variation. Solving quadratic equations, basic rules of factoring, power rule, exponents and radicals, radian measure, arc length, and rotation. Pythagorean Theorem and the six trigonometric ratios are also covered.

MAT 148 Mathematics for Technicians II | MAT 148 Sample Syllabus
Prerequisite: MAT 147
Credits: 4 (NOTE: Restricted to Applied Manufacturing Option (MPA), Electronics Engineering Technology- Mechatronics Option (EEMO), Manufacturing Technology (MP), Electronics Engineering Technology – Biomedical Instrumentation Option (EEBI), Electronics Engineering Technology – Photonics Option (EEPH), Energy Utility Technology Certificate – (EUTC))
This course covers applied mathematical and statistical concepts and methods: Topics include Trigonometry, parametric, and polar graphs; Trigonometric identities and equations; Exponential and logarithmic functions; Complex numbers and their applications; Series, sequences and the binomial theorem; Introduction to statistics and probability; Process Control, Correlation and Regression Analysis; Derivatives of algebraic functions.

MAT 100 College Algebra | MAT 100 Sample Syllabus
Prerequisite: QMAT placement score > 32 or
Corequisite: MAT 097 College Algebra Corequisite
Credits: 3
This course covers advanced algebra topics. Students perform arithmetic operations on rational expressions; solve equations with fractions; factor expressions; simplify complex fractions; simplify exponential expressions, roots, radicals, and rational exponents; solve linear systems using several techniques; use the midpoint and distance formulas; recognize and graph the equation of a circle; solve linear and absolute value inequalities; solve quadratic equations by completing the square and by using the quadratic formula; solve equations containing radicals or absolute values; and perform arithmetic operations on radical expressions and complex numbers.

MAT 123 College Mathematics I: Pre-Calculus | MAT 123 Sample Syllabus
Prerequisite: MAT 100 or appropriate placement score
Credits: 3
This course focuses on the knowledge and skills necessary for advanced mathematics. Students expand binomial expressions using the binomial theorem; solve non-linear, and rational inequalities and write their solutions using interval notation; determine and write linear equations in several forms; explain the concept of function; graph functions using symmetry test; recognize and graph functions, including constant, linear, quadratic, polynomial, rational, exponential, and logarithmic functions; use function transformation techniques; perform composition and arithmetic operations on functions; find and graph inverses of functions; use properties of logarithms; and solve logarithmic and exponential equations.

MAT 124 College Mathematics II: Trigonometry | MAT 124 Sample Syllabus
Prerequisite: MAT 123 or appropriate placement score
Credits: 3
Students solve right and oblique triangles and related applications; perform vector computations and use vector concepts to solve applications; determine the values of trigonometric ratios of angles and the values of inverse trigonometric ratios of real numbers; work with angles measured in degrees-minutes-seconds or radians; solve uniform circular motion problems; learn the traditional trigonometric identities and use them to prove other identities; perform transformations of basic trigonometric graphs; write equations to describe specific instances of harmonic motion; and solve trigonometric equations.

MAT 125 Discrete Mathematics | MAT 125 Sample Syllabus
Prerequisite: MAT 123 or appropriate placement score
Credits: 3
This course provides an introduction to the basic concepts in Discrete Mathematics. Topics include predicate and propositional calculus, sets, proof techniques, permutations and combinations, probability, relations, closure, partial order, functions, graph connectivity and shortest paths, and an introduction to languages, grammars and nondeterministic finite-state machines.

MAT 233 Calculus I | MAT 233 Sample Syllabus
Prerequisite: MAT 124 or appropriate placement score
Credits: 4
This course begins with a review of functions and functional notation. After introducing the limit and continuity theorems on an intuitive basis, the study of differentiation begins. Typical derivative formulae are applied to polynomial, rational, trigonometric, implicit, logarithmic, exponential, and inverse trigonometric functions. Application topics include extrema, related rates, curve sketching, and velocity and acceleration. The basic rules of integration and the substitution method are introduced along with Riemann Sums and the Fundamental Theorem of Calculus.

MAT 234 Calculus II | MAT 234 Sample Syllabus
Prerequisite: MAT 233
Credits: 4
This course focuses on expanded methods of integration and their application. Derivatives of the exponential, logarithmic and inverse trigonometric functions as well as their antiderivatives will be reviewed. Students learn to compute the customary antiderivatives of functions and apply antidifferentiation to such areas as volumes, moments, centroids, arc lengths and surfaces of revolution. Students will be introduced to differential equations. The use of L’Hopital’s Rule and the evaluation of improper integrals are examined. The convergence tests of infinite series as well as the Power, Taylor and Maclaurin series are analyzed.

MAT 235 Calculus III | MAT 235 Sample Syllabus
Prerequisite: MAT 234
Credits: 4
This course covers conic sections, rotation of axis, plane curves, parametric equations, vectors; polar, cylindrical, and spherical coordinates and graphs; vector-valued functions, differentiation, and integration; functions of several variables, partial derivatives, gradients; applications of extrema of functions, Lagrange multipliers; multiple integrations; area, volume, center of mass, moment of inertia, change of variables, Jacobians; Green’s divergence and Stokes’ theorems. Students learn to use calculus to solve engineering and scientific problems. The course concludes with some elementary differential equations.

MAT 237 Probability & Statistics for Engineers and Scientists | MAT 237 Sample Syllabus
Prerequisite: MAT 234
Credits: 3
This course focuses on statistics and engineering. It covers interpretation, description, and treatment of data; probability and probability distributions; binomial, geometric, and hypergeometric methods; Poisson processes; gamma, beta, and Weibull distribution; populations and samples; inferences, hypotheses, and significance tests; Bayesian estimates; curve fitting; the method of least squares; curvilinear regression, correlation, and experimental design. Students use calculators and statistical software to solve statistical problems.

MAT 238 Differential Equations | MAT 238 Sample Syllabus
Prerequisite: MAT 235
Credits: 3
This course covers definition of differential equations, solution of differential equations, separation of variables, homogeneous and nonhomogeneous solutions, Wronskian, second and higher order equations, solution of systems of linear differential equations, numerical methods, linear independence, the Laplace transform, transforms of derivatives, derivatives of transforms, the Gamma function, inverse transforms, and convolution theorem. Students use mathematical software to solve differential equations for numerical methods.

MAT 243 Linear Algebra | MAT 243 Sample Syllabus
Corequisite: MAT 238
Credits: 3
This course covers systems of linear equations, matrices, reduced echelon forms, vectors in Rn, linear independence and transformations, matrix operations, inverse of a matrix, determinants, vector space, rank, subspaces, bases, eigen vectors and eigen values, the characteristic equations, diagonalization, complex eigen values, numerical methods for solving linear systems, and orthogonality. Students learn to use linear algebra to solve problems in differential equations, statistics, and engineering design. Students also use mathematical software to solve higher order systems of equations and matrices.

What is an Emporium math class like?
An Emporium math class is like an online course that is completed in a computer classroom at QCC. Students will practice their math skills using software that will enable them to view examples, get help solving problems, and watch videos of teachers explaining material and modeling problems. Since the course will meet at QCC, students will also have a teacher in the classroom to answer questions and provide individualized instruction. The teacher may also provide mini-lectures and/or facilitate group activities.

Are Emporium math classes flexible and/or personalized?
One of the great things about an Emporium class, is that students are allowed to accelerate through the course at their own pace (as long as they meet or surpass the minimum due dates listed in the syllabus). Students will also have the option of taking a pre-test before every module in the course. If the student scores at least an 80% on a pre-test, they will be able to skip the module, leaving them with more time to spend on topics they do not yet understand. Note: All module tests will be proctored.

The student will also be required to earn a grade of at least 80% on each module test and non-media homework assignment, in order to advance throughout the course. In order to earn the 80%, multiple attempts on homework problems and module tests are allowed. Students will be able to ask questions and practice similar examples in between attempts, until they are ready to try again. The flexibility in the course allows students to truly have a personalized experience. Students are in charge of setting their own goals for how fast they move through the course.

As an added bonus, if the student completes all three module tests with a grade of at least 80% on each, they will have satisfied the final exam requirement for the course and will not need to take an additional final exam during the final exam period. However, if the student does not finish all three modules in the course, they will need to take the final exam during the final exam period, in order to try to pass the course. The minimum passing grade in a stand-alone developmental course is a “C.”

Attendance—Including Additional, Weekly Session Requirement
Please remember that this is not an online course. Since receiving additional explanation/help from the instructor is expected and encouraged, live attendance in this course is required. Students will be responsible for attending classroom meetings and an additional, 50-minute session each week. In the Fall/Spring semester, the additional weekly session is required during weeks 3-14, and the requirement can be waived if the student is at least a full week ahead in the course. The additional weekly session is provided free of charge and is a requirement to help ensure students are spending enough time working on math in an environment that has all the necessary technology and assistance to help them succeed. During the extra session, students will continue working through their course. If the student ever misses a class or cannot complete an extra session during a particular week, they can make up the missed time in the following week. Students are allowed to complete the extra weekly session while visiting the Math Center. To view the Math Center hours, please refer to the Math Center website. Note: Students are not allowed to complete module tests in the Math Center.

What supplies are needed for Emporium classes?
In terms of supplies for the course, students will need an Access Code to use MyLab Math. Students will also need the corresponding Video Organizer (which is a notebook that contains the information from the lecture videos), and a pair of headphones/earbuds to connect to the computer to listen to video lectures during class. Please go to the QCC Bookstore's website to view the Video Notebook and MyLab Math Access Code information for each particular course on the QCC Bookstore Website. Students in MAT 095 (Beginning Algebra) are allowed to use a handheld, scientific (non-graphing) calculator. (We recommend the TI-30XIIS calculator.)

Students who have been away from math for a while may find the Basic Math Refresher a good place to review previously-learned math topics, such as:

• fractions
• decimals
• percentages
• proportions
• order of operations

The refresher is not a math course. Instead, it is a self-guided and self-paced series of short videos, practice questions with immediate feedback, and skill checks that students can work on covering these basic math topics. Although completing the refresher does not serve as a prerequisite for any math course, it is offered at no cost to any QCC student. To request access to the Basic Math Refresher, students should email the Math Center.

For any QCC student

• who plans to take the QMAT placement test and wants to practice/review before taking it, or
• who has been away from math for a while, are perhaps anxious about taking a math course, and wants to review some basic math skills (i.e., fractions, decimals, percentages, order of operations) before the start of the semester,

the Math Dept offers a Pre-semester Math Refresher. During the few weeks leading up to the start of a semester, the Math Center will be open for the refresher.

Simply drop-in (no appointment necessary) to the Math Center to receive help from a friendly math tutor in a welcoming environment when you get stuck or have a question. Computers are available in the Math Center, or bring your own laptop. You'll be able to access the QMAT practice tests that the Advising office emailed to you. Or if a student wishes to work on the Basic Math Refresher, a free access code will be provided.

Towards the goal of helping students complete their program's college-level math requirement, the Math Dept now offers several co-requisite math courses, such as:

• MAT 121 + MAT 051 Topics in Math
• MAT 122 + MAT 052 Statistics
• MAT 100 + MAT 097 College Algebra

A co-requisite math course typically consists of specific remedial math topics covered just-in-time so students can be successful in the related college-level math topics that are covered. For example, simplifying fractions and rounding decimals are taught immediately before probability is covered in Statistics.

Co-requisite courses consist of five (5) credits, made up of three (3) credits of college-level math and two (2) credits of remedial math. Only the college-level course meets a student's program requirements, applies towards graduation requirements, and/or is transferable to other colleges or universities.

A student who successfully completes a co-requisite math course potentially saves time and money!

Note: If a student's program requires both a STEM-related math course and a non-STEM math course, the Math Dept strongly recommends the student complete the STEM-related math course before taking the non-STEM math course. This would prevent a student from taking two co-requisite math courses. Please speak to Advising for more information.

The Math Center is one of our best resources on campus. It offers free, drop-in tutoring for currently enrolled QCC students taking any math course.

The Math Dept has its own YouTube channel called QCC Math. The channel consists of various playlists, where each playlist is dedicated to a specific QCC math course. 

• MAT 095 Beginning Algebra Playlist
• MAT 100 College Algebra Playlist
• MAT 122 Statistics Playlist
• MAT 123 Pre-Calculus Playlist
• MAT 124 Trigonometry Playlist
• MAT 233 Calculus I Playlist
• MAT 237 Probability and Statistics for Engineers and Scientists Playlist

Dr. Ben Benton 
Dean of Math and Science | 508.854.2835 
bbenton@qcc.mass.edu 

Michelle Sheehan 
Administrative Assistant I 508.854.2783 
msheehan@qcc.mass.edu

Full-time faculty in the mathematics department: