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This course is designed to orient undergraduate math majors to the university and to their chosen field. Students will learn about the mathematics program, the mathematics faculty and their research interests, careers in math-related areas, internship opportunities, and university resources.
Pre-req: Math Majors Only.
The Number and Operations course for elementary and middle school teachers examines the three main categories in the Number and Operations strand of Principles and Standards of School Mathematics (NCTM) -- Understanding numbers, representations, relationships, and number systems; the meanings of operations and relationships among those operations; and reasonable estimation and fluent computation. No credit in Science or Engineering.
Pre-req: Elementary Education Minors and BLA-Education Concentration majors only.
This course seeks to support students in furthering their understanding of elementary mathematics concepts. The goal is for students to not only pass the MTEL for elementary mathematics, but to lay the groundwork for graduate work in elementary mathematics education. Specifically, we use an integrated approach to algebra that draws on real-world data to the extent possible. To this end, learners will gain experience in selecting and developing a number of data representations, organizing data, looking for patterns in the data and, finally, using words, symbolic notation, graphs and tables to generalize those patterns. No credit in Science or Engineering.
An introduction to the mathematics concepts and skills important in modern society, even for non-technical pursuits. The course will emphasize conceptual understanding as well as a facility in performing elementary computations. Topics to be examined will include types of reasoning, problem-solving methods, techniques of estimation, algebraic essentials, and the nature of probability and statistics. No credit in Science or Engineering.
This course provides supplemental instruction in mathematics to students whose Elementary Algebra Accuplacer exam scores indicate the need for such instruction. The credits in this course can not be used to satisfy the credits required for graduation, but may be used to satisfy the credits required for full time student status.
Co-Req: 92.111 Quantitative Reasoning.
Intended for students with little or no background in basic algebra or whose background is not current. Topics covered include: the real number system, factoring fractions, linear equations, functions, graphs, systems of equations, and the quadratic equation. Students will not receive credit for this course toward any degree program at the University of Massachusetts Lowell.
Review of algebra. The Real Numbers, inequalities and intervals on the number line, factoring, radical notation, properties of exponents, scientific notation, and operations on rational expressions. Function definition and graph of linear/nonlinear functions such as quadratic, cubic, absolute value, piecewise-defined, rational, and power function. Additional topics with functions included such as transformations of graphs and symmetry, composite functions, one-to-one and inverse functions. Solving linear and quadratic equations algebraically and graphically. Solving systems of equations in two variables algebraically and graphically. Modeling systems of equations in three variables and solving them analytically and with matrices using TI-84 implementation. Modeling with linear as well as quadratic and power functions with the aid of a graphing calculator and Excel spread sheets. Business applications are included.
Taken simultaneously with MATH.1210, this 1-credit course offers students taking MATH.1210 supplemental instructions to foster a greater opportunity for successful completion of Management Precalculus. The course credit cannot be used to satisfy the credits required for graduation, but may be used to satisfy credits required for full time student status.
Co-Req: MATH.1210 Management Pre-Calculus
Review of difference quotient, least squares modeling, limit of difference quotient, differential calculus: derivatives, differentials, higher-order derivatives, implicit differentiation, relative and absolute maxima and minima of functions, and applications of derivatives to business and economics. Integrals and applications to business. No credit in Science or Engineering.
Pre-req: MATH.1200 Precalculus Mathematics I, or MATH.1210 Management Precalculus, or MATH.1270 Preparation for Calculus.
Taken simultaneously with MATH.1220, this 1-credit course offers students taking MATH.1220 supplemental instructions to foster a greater opportunity for successful completion of Management Calculus. The course credit cannot be used to satisfy the credits required for graduation, but may be used to satisfy credits required for full time student status.
Co-Req: MATH.1220 Management Calculus.
Provides a review of pre-calculus algebra and trigonometry integrated with the first half of Calculus I: limits, continuity, derivatives, basic derivative formulas, chain rule, implicit differentiation.
Taken simultaneously with MATH.1280, this 1-credit course offers students retaking MATH.1280 supplemental instructions to foster a greater opportunity for successful completion of Calculus IA. The course credit cannot be used to satisfy the credits required for graduation, but may be used to satisfy credits required for full time student status.
Provides a review of pre-calculus, algebra and trigonometry integrated with the second half of Calculus I. Inverse trig functions and their derivative, logarithmic functions and their derivative, related rates, L'Hospital's Rule, optimization problems, curve sketching, linearization, Newton's Method, hyperbolic functions and their derivative, antiderivatives. Completion of this course is equivalent to MATH.131 0 Calculus I.
Pre-Req: MATH 1280 Calculus IA, or CA1A student group waiver or a grade of CR in NONC CALC1A.
Taken simultaneously with MATH.1290, this 1-credit course offers students retaking MATH.1290 supplemental instructions to foster a greater opportunity for successful completion of Calculus IA. The course credit cannot be used to satisfy the credits required for graduation, but may be used to satisfy credits required for full time student status.
Serves as a first course in calculus. Functions, limits, continuity, derivatives, rules for differentiation of algebraic and transcendental function; chain rule, implicit differentiation, related rate problems, linearization, applied optimization, and curve sketching. Introduction to area and integration.
Serves as a continuation of Calculus I. Integration and techniques of integration including the substitution method, integration by parts, trigonometric integrals, trigonometric substitution, integration of rational functions by partial fractions, numerical integration, and improper integrals. Volumes using cross-sections, the disk method, the washer method and the shell method. Arc length and surface area. Infinite series, power series, Maclaurin and Taylor series. Polar coordinates and areas and lengths in polar coordinates.
Pre-Req: MATH 1290 Calculus IB, MATH 1310 Calculus I, or a grade of CR in NONC CALC1.
This is a single variable calculus course with applications to the life sciences. Review of basic algebra, trigonometry, functions and graphs. Limits and derivatives, including differentiation rules, curve sketching and optimization problems. Implicit differentiation. Study of exponential and logarithmic functions motivated by growth, decay and logistic modes. Introduction to integration, techniques, applications and the fundamental theorem.
This course is a continuation of MATH.1380. Review of integration and methods. Solving systems of linear equations. Use and application of matrices including inverses, determinants, eigenvalues and eigenvectors. Solving difference equations. Differential and integral calculus for functions of several variables, including maximum-minimum problems, partial derivatives. Method of least squares. First-order differential equations. Higher-order and systems of linear differential equations. Stability and trajectories using matrices. Population models and approximation techniques. Biology majors only.
Pre-req: MATH.1380 Calculus for the Life Sciences I.
This course covers the same topics as MATH.1310 Calculus I, but in an enriched environment.
This course covers the same topics as MATH.1320 Calculus II, but in an enriched environment.
Pre-req: MATH.1410 Honors Calculus I, or permission of Instructor.
This course is not so much about the mathematics of formulas, equations, rules and errors, as about mathematics that can be experienced: counted, drawn, seen, created; quite simply: played with. Officially, we will encounter concepts of combinatorics, geometry, number theory and Boolean logic. Unofficially, we will experiment with puzzles and patterns and develop as much mathematics from them as we can. Prerequisites: high school mathematics and willingness to explore. No credit in science or engineering. This course satisfies the Quantitative Reasoning requirement.
Engage in lab-based activities designed to strengthen their problem-solving skills and expand knowledge of the topics in secondary mathematics, focusing especially on topics from precalculus and the transition to calculus. Explore a variety of contexts that can be modeled using families of functions. Topics include conic sections, parametric equations and polar equations. Multiple representations, transformations, data analysis techniques and interconnections among geometry, probability and algebra. Quantitative approaches and building relationships between discrete and continuous reasoning will be recurrent themes.
Co-Req: MATH 1320
Presents propositional logic, combinatorics, methods of proof, mathematical systems, algebra of sets, matrix algebra, relations and functions, recursion and generating functions, applications to computer science, and graph theory.
Pre-Req: MATH 1310 Calculus I or MATH 1380 Calculus for Life Sciences.
Elementary set theory and solution sets of systems of linear equations. An introduction to proofs and the axiomatic methods through a study of the vector space axioms. Linear analytic geometry. Linear dependence and independence, subspaces, basis. Inner products. Matrix algebra. Applications of the above will also be discussed.
Pre-Req: MATH 1320 Calculus II.
Linear transformations. Linear operators, change of basis, inner product and the diagonalization problem. Quadratic forms. Convex sets and geometric programming, input/output models for an economy, Markov chains, other applications of linear algebra.
Pre-Req: MATH.2210 Linear Algebra I.
This is a mathematics content course which covers the geometry/measurement strands of the Massachusetts Curriculum Frameworks in Mathematics at a collegiate level. The goal is not only to prepare students for the elementary mathematics MTEL, but to lay the groundwork for graduate work in elementary mathematics education. The course centers around "Big Ideas" such as Equivalence, Proportionality, Transformations; and Shapes & Solids. No credit in Science or Engineering.
Extends the concepts of Calculus I and II that deal with functions of a single variable to multi-variable functions, vector-valued functions and vector fields. Vectors and vector-valued functions, the dot and cross products, curves in space and the calculus of vector-valued functions. Multi-variable functions, limits, continuity, and differentiation. Partial derivatives, directional derivatives, the gradient, Lagrange multipliers and optimization. Double and triple integrals in Cartesian, polar and spherical coordinates. Vector fields and the fundamental theorems of vector calculus developed, line and surface integrals, Green's theorem, Stokes's theorem, and the divergence theorem.
An introduction to mathematics related software. Topics from Calculus & Differential Equations will be explored using a symbolic package like Maple. the course will also introduce LaTeX, the standard for typesetting mathematics.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Differential Equations or MATH 2360 Eng Differential Equations.
Topics include methods of solutions for linear and non-linear first order differential equations, linear second order differential equations, higher order linear differential equations, systems of first-order differential equations. Laplace transforms. Numerical methods. Applications to physical systems.
Introduction to differential equations with an emphasis on engineering applications. Topics include first-order equations, higher-order linear equations with constant coefficients, and systems of first-order equations. Applications of each topic are introduced and qualitative, analytical, and numerical solution techniques are studied. Laplace transform methods are discussed. The software package MATLAB is used throughout the course for both analytical and numerical calculations.
Covers the same topics as MATH.2310 Calculus II, but in an enriched environment.
Pre-Req: MATH.1420 Honors Calculus II or permission of instructor
Introduction to differential equations. Topics include first-order equations, second-order and higher-order linear equations, systems of first-order linear equations with constant coefficients, and Laplace transforms.
Pre-Req: MATH 1320 Calculus II.
This course will introduce basic programming concepts using MATLAB as the programming environment. Topics include an introduction to MATLAB, array manipulation, graphics, script files, data input and output, relational and logical operators, conditional statements, loops, and iterative procedures. Additional topics will be discussed as time permits. Additional topics will be chosen from the following: finding roots of nonlinear equations, random number generation, Markov processes, simple statistics, interpolation, and the basics of Fourier analysis.
An introduction to descriptive statistics, graphing and data analysis, probability laws, discrete and continuous probability distributions, correlation and regression, inferential statistics. No credit in Science or Engineering. Meets Core Curriculum Essential Learning Outcome for Quantitative Literacy (QL).
Discusses vector analysis, Green's Theorem, Divergence Theorem, Stokes' Theorem, Fourier series, integrals, and partial differential equations of physics and engineering.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Differential Equations or MATH 2360 Eng Differential Equations.
Introduces students to matrix algebra, solution of systems of linear equations, eigenvalues and eigenvectors, solution of differential equations by matrix methods, series solution of differential equations, Bessel and Legendre functions, and Sturm-Liouville problems.
Examines graph theory, trees, algebraic systems, Boolean algebra, groups, monoids, automata, machines, rings and fields, applications to coding theory, logic design, and sorting.
Pre-Req: MATH.3210 Discrete Structures I.
An introduction to symbolic logic. Symbolic logic provides a framework of formal reasoning with applications in mathematics, cognitive science, computer science and philosophy. Topics include propositional logic, boolean algebras and rings, first-order logic and systems of deduction. Time permitting, we will touch on Tarski's notion of model, and the completeness and incompleteness theorems of Godel.
Basic concepts of data. Linear lists, strings, arrays, and orthogonal lists. Trees and graphs. Storage systems and structures. Storage allocation and collection. Multilinked structures. Symbol tables, searching and sorting (ordering) techniques. Not for math majors.
Pre-Req: MATH 2310 Calculus III.
Focuses on the theory and application of numerical techniques including error analysis. Also discusses solution of linear, nonlinear and differential equations, interpolation, numerical integration, and curve fitting. Computer solutions are emphasized.
Computer analysis of data derived from research conducted in physical, social, and life sciences. Data preparation. Data modification, file manipulation, and descriptive statistics using SPSS. Programming ability is not required. No credit in Science or Engineering.
Student works with an advisor to develop a proposal for a senior project that will be carried out as part of MATH.4750 Senior Seminar II. Generally taken during the spring of the junior year. Prerequisite: Permission of instructor.
Intended for students having completed 2 full years of physics and math, this course is designed to develop competency in the applied mathematical skills required of junior and senior level physics majors. Covering topics involving infinite series, power series, complex numbers, and linear algebra along with vector and Fourier analysis, students will be trained with the rigor required to solve a wide range of applications in the physical sciences. Physics majors only.
Pre-req: MATH.2310 Calculus III, and MATH.2340 Differential Equations, or MATH.2360 Engineering Differential Equations, and PHYS.1440 Physics II, or PHYS.1640 Honors Physics II.
Introduction to experimental design, data analysis and formal statistical procedures from an applied point of view.
Provides a one-semester course in probability and statistics with applications in the engineering sciences. Probability of events, discrete and continuous random variables cumulative distribution, moment generatory functions, chi-square distribution, density functions, distributions. Introduction to estimation, hypothesis testing, regression and correlation. No credit for both MATH.3860 and MATH.4070.
The real numbers, completeness, sequences of real numbers, functions, continuity, uniform continuity, differentiability, the Riemann integral, series or real numbers, sequences and series of functions, uniform convergence, power series.
Pre-req: MATH 1320 Calculus II and MATH 3210 Discrete Structures I.
Addresses the topics of probability, random variables, discrete and continuous densities, expectation and variance, special distributions (binomial, Poisson, normal, etc.), moment generating functions, joint and conditional distributions, transformations of variables, sampling, and the central limit theorem.
Pre-req: MATH 2310 Calculus III, or MATH 2260 Calculus D, and MATH 3210 Discrete Structures I.
This course explores the roles of mainframes, PC's and hand calculators in instruction, examine some of the available software and consider their use in a variety of areas of secondary mathematics, such as algebra, geometry (Euclidean and analytic), probability and statistics and introductory calculus.
No credit in Science or Engineering.
A first course in theory of analytic functions of one complex variable: complex differentiability and the Cauchy-Riemann equations, Cauchy Integral Theorem and Cauchy Integral Formula, Taylor and Laurent series, zeroes of analytic functions and uniqueness, the maximum modulus principle, isolated singularities and residues. Applications.
Studies congruencies and the Chinese Remainder Theorem, Primitive roots, quadratic reciprocity, approximation properties of continued fractions, Pell's equation. Recent application of number theory such as primality testing, cryptology, and random number generation will also be covered.
Pre-Req: MATH 2210 Linear Algebra I or MATH 3210 Discrete Structures I.
A project -based course starting with an introduction to the basic features of Mathematica. A project that allows the student to focus on certain features in more detail is required and occupies the second half of the course.
Focuses on: mathematical resources, ability to use heuristics, the student's beliefs about the use of mathematics to solve problems, and the student's self-confidence as a problem solver. Effective strategies for incorporating problem solving in the curriculum will also be discussed.
Elementary group theory, groups, cosets, normal subgroups, quotient groups, isomorphisms, homomorphisms, applications.
Metric spaces, topological spaces, connectedness, compactness, the fundamental group, classifications of surfaces, Brouwer's fixed point theorem.
Pre-req: MATH 4030 Mathematical Analysis or MATH 5010 Real Analysis
This course is designed for current and prospective geometry teachers. In addition to the development of Euclidean geometry, students will become familiar with geometry applications in Geometer's Sketchpad software, and to a lesser degree with other geometry software applications including Geogebra, and Cabri. There will be an introduction to spherical and hyperbolic geometry and triangle measurements will be computed for each. Calculus based derivations of area and volume for surfaces and solids will be generated and related to Euclidean geometry topics.
Examines ancient numeral systems, Babylonian and Egyptian mathematics, Pythagorean mathematics, duplication, trisection, and quadrature, Euclid's elements and Greek mathematics after Euclid, Hindu and Arabian mathematics, European mathematics from 500 to 1600, origins of modern mathematics, analytic geometry, the history of calculus. Also covers the transition to the twentieth century and contemporary perspectives.
Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial dimensions): the wave equation, the heat/diffusion equation, the Laplace/Poisson equation. Initial value problems - solution formulas. Fundamental solutions. Green's functions. Eigenfunction expansion method for initial-boundary and boundary value problems.
Pre-Req: MATH 2340 Differential Equations or MATH 2360 Eng Differential Equations.
Representation of Signals: Fourier analysis, fast Fourier transforms, orthogonal expansions. Transformation of signals: linear filters, modulation. Band-limited signals. Sampling. Uncertainty principle. Windows and extrapolation. Applications to medical imaging and array processing.
Applications of mathematics to real life problems. Topics include dimensional analysis, population dynamics wave and heat propagation, traffic flow.
An introduction to creation and manipulation of databases and statistical analysis using SAS software. SAS is widely used in the pharmaceutical industry, medical research and other areas. Cannot be used as a Math Elective.
Undergraduate seminar on advanced mathematical topics. Students are required to develop an understanding of an advanced subject beyond the scope of an existing course or synthesize two or more different areas form their curriculum. Students are required to participate in the seminar, present their results to the Department and write a substantial thesis in their topic area. Essential course elements include library research, original research, and both verbal and written exposition. The first semester is a graduation requirement for majors in mathematics.
Pre-Req: MATH.3750 or MATH.4740 Senior Seminar I.
An optional second semester seminar to allow for continuation of study initiated in Senior Seminar I.
Pre-Req: MATH.4750 Senior Seminar II.
Point estimation, confidence intervals, hypothesis testing. Two-sample t-test. Correlation and linear regression. The bivariate normal distribution. Analysis of variance for one-and two-way designs. F tests. Nonparametric methods. Chi-squared tests for contingency tables. Generalized likelihood ratio. C.R. bound. Consistency.
Pre-req: MATH.4070 Probability and Mathematical Statistics I.
Individual study for the student desiring more advanced or more specialized work. Course may not be substituted for scheduled offerings. Prerequisite: Permission of Department Chair.
Individual study for the student desiring more advanced or more specialized work in algebra. May be repeated for a total of six semester credits. Course may not be substituted for scheduled offerings.
Individual study for the student desiring more advanced or more specialized work in Statistics. May be repeated for a total of six semester credits. Course may not be substituted for scheduled offerings. Prerequisite: Permission of Department Chair.
Unpaid internship in the Department of Mathematical Sciences. This allows students to receive up to 3 (free elective) credits while working on an approved project. Students who have a position and who wish to take advantage of this Practicum should see the department Internship Coordinator.