This advance is advised to acclimatize undergraduate algebraic majors to the university and to their called field. Acceptance will apprentice about the mathematics program, the mathematics adroitness and their assay interests, careers in math-related areas, internship opportunities, and university resources.
Pre-req: Algebraic Majors Only.
The Cardinal and Operations advance for elementary and average academy agents examines the three capital categories in the Cardinal and Operations fiber of Principles and Standards of Academy Mathematics (NCTM) — Compassionate numbers, representations, relationships, and cardinal systems; the meanings of operations and relationships amid those operations; and reasonable admiration and chatty computation. No acclaim in Science or Engineering.
Pre-req: BA-ED Majors only.
This advance seeks to abutment acceptance in furthering their compassionate of elementary mathematics concepts. The ambition is for acceptance to not alone canyon the MTEL for elementary mathematics, but to lay the accomplishments for alum assignment in elementary mathematics education. Specifically, we use an chip access to algebra that draws on real-world abstracts to the admeasurement possible. To this end, learners will accretion acquaintance in selecting and developing a cardinal of abstracts representations, acclimation data, attractive for patterns in the abstracts and, finally, appliance words, allegorical notation, graphs and tables to generalize those patterns. No acclaim in Science or Engineering.
Pre-req: BA-ED Majors only.
An accession to the mathematics concepts and abilities important in avant-garde society, alike for non-technical pursuits. The advance will accent conceptual compassionate as able-bodied as a adeptness in assuming elementary computations. Capacity to be advised will accommodate types of reasoning, analytic methods, techniques of estimation, algebraic essentials, and the attributes of anticipation and statistics. No acclaim in Science or Engineering.
This advance provides added apprenticeship in mathematics to acceptance whose Elementary Algebra Accuplacer assay arrangement announce the charge for such instruction. The credits in this advance can not be acclimated to amuse the credits appropriate for graduation, but may be acclimated to amuse the credits appropriate for abounding time apprentice status.
Co-Req: 92.111 Quantitative Reasoning.
Intended for acceptance with little or no accomplishments in basal algebra or whose accomplishments is not current. Capacity covered include: the complete cardinal system, factoring fractions, beeline equations, functions, graphs, systems of equations, and the boxlike equation. Acceptance will not accept acclaim for this advance against any amount affairs at the University of Massachusetts Lowell.
Review of algebra. The Complete Numbers, inequalities and intervals on the cardinal line, factoring, abolitionist notation, backdrop of exponents, accurate notation, and operations on rational expressions. Action analogue and blueprint of linear/nonlinear functions such as quadratic, cubic, complete value, piecewise-defined, rational, and adeptness function. Additional capacity with functions included such as transformations of graphs and symmetry, blended functions, one-to-one and changed functions. Analytic beeline and boxlike equations algebraically and graphically. Analytic systems of equations in two variables algebraically and graphically. Clay systems of equations in three variables and analytic them analytically and with matrices appliance TI-84 implementation. Clay with beeline as able-bodied as boxlike and adeptness functions with the aid of a graphing calculator and Excel advance sheets. Business applications are included.
Taken accompanying with MATH.1210, this 1-credit advance offers acceptance demography MATH.1210 added instructions to advance a greater befalling for acknowledged achievement of Management Precalculus. The advance acclaim cannot be acclimated to amuse the credits appropriate for graduation, but may be acclimated to amuse credits appropriate for abounding time apprentice status.
Co-Req: MATH.1210 Management Pre-Calculus
Review of aberration quotient, atomic squares modeling, complete of aberration quotient, cogwheel calculus: derivatives, differentials, higher-order derivatives, complete differentiation, about and complete maxima and minima of functions, and applications of derivatives to business and economics. Integrals and applications to business. No acclaim in Science or Engineering.
Pre-req: MATH.1200 Precalculus Mathematics I, or MATH.1210 Management Precalculus, or MATH.1270 Alertness for Calculus, or MATH.1280 Calculus IA, or MATH.1290 Calculus IB,or ALEKS account of 67 or higher.
Taken accompanying with MATH.1220, this 1-credit advance offers acceptance demography MATH.1220 added instructions to advance a greater befalling for acknowledged achievement of Management Calculus. The advance acclaim cannot be acclimated to amuse the credits appropriate for graduation, but may be acclimated to amuse credits appropriate for abounding time apprentice status.
Co-Req: MATH.1220 Management Calculus.
A assay of precalculus (algebra and trigonometry) calm with development of botheration analytic skills. No acclaim in Science or Engineering.
Provides a assay of pre-calculus algebra and trigonometry chip with the aboriginal bisected of Calculus I: limits, continuity, derivatives, basal acquired formulas, alternation rule, complete differentiation. Acceptance are accepted to accept taken pre-calculus and trigonometry in adjustment to be acknowledged in this course.
Taken accompanying with MATH.1280, this 1-credit advance offers acceptance retaking MATH.1280 added instructions to advance a greater befalling for acknowledged achievement of Calculus IA. The advance acclaim cannot be acclimated to amuse the credits appropriate for graduation, but may be acclimated to amuse credits appropriate for abounding time apprentice status.
Provides a assay of pre-calculus, algebra and trigonometry chip with the additional bisected of Calculus I. Changed accurate functions and their derivative, logarithmic functions and their derivative, accompanying rates, L’Hospital’s Rule, access problems, ambit sketching, linearization, Newton’s Method, abstract functions and their derivative, antiderivatives. Achievement of this advance is agnate to MATH.131 0 Calculus I.
Pre-req: MATH.1280 Calculus IA.
Taken accompanying with MATH.1290, this 1-credit advance offers acceptance retaking MATH.1290 added instructions to advance a greater befalling for acknowledged achievement of Calculus IA. The advance acclaim cannot be acclimated to amuse the credits appropriate for graduation, but may be acclimated to amuse credits appropriate for abounding time apprentice status.
Serves as a aboriginal advance in calculus. Functions, limits, continuity, derivatives, rules for adverse of algebraic and abstruse function; alternation rule, complete differentiation, accompanying amount problems, linearization, activated optimization, and ambit sketching. Accession to breadth and integration. Acceptance are accepted to accept taken pre-calculus and trigonometry in adjustment to be acknowledged in this course.
ALEKS Algebraic Placement 76-100 (Students repeating advance may ask for permission cardinal from the department) or pre-req of MATH.1290.
Serves as a assiduity of Calculus I. Affiliation and techniques of affiliation including the barter method, affiliation by parts, algebraic integrals, algebraic substitution, affiliation of rational functions by fractional fractions, afterwards integration, and abnormal integrals. Volumes appliance cross-sections, the deejay method, the washer adjustment and the carapace method. Arc breadth and apparent area. Absolute series, adeptness series, Maclaurin and Taylor series. Arctic coordinates and areas and lengths in arctic coordinates.
Pre-Req: MATH 1290 Calculus IB, MATH 1310 Calculus I, or a brand of CR in NONC CALC1.
This is a distinct capricious calculus advance with applications to the activity sciences. Assay of basal algebra, trigonometry, functions and graphs. Banned and derivatives, including adverse rules, ambit abstraction and access problems. Complete differentiation. Abstraction of exponential and logarithmic functions motivated by growth, adulteration and logistic modes. Accession to integration, techniques, applications and the axiological theorem.
Pre-req: Biology, and Pre-Med, and Pre-Dental Majors.
This advance is a assiduity of MATH.1380. Assay of affiliation and methods. Analytic systems of beeline equations. Use and appliance of matrices including inverses, determinants, eigenvalues and eigenvectors. Analytic aberration equations. Cogwheel and basal calculus for functions of several variables, including maximum-minimum problems, fractional derivatives. Adjustment of atomic squares. First-order cogwheel equations. Higher-order and systems of beeline cogwheel equations. Stability and trajectories appliance matrices. Citizenry models and approximation techniques. Biology majors only.
Pre-req: MATH.1380 Calculus for the Activity Sciences I.
This advance covers the aforementioned capacity as MATH.1310 Calculus I, but in an accomplished environment.
This advance covers the aforementioned capacity as MATH.1320 Calculus II, but in an accomplished environment.
Pre-req: MATH.1410 Honors Calculus I, or permission of Instructor.
This advance is not so abundant about the mathematics of formulas, equations, rules and errors, as about mathematics that can be experienced: counted, drawn, seen, created; absolutely simply: played with. Officially, we will appointment concepts of combinatorics, geometry, cardinal approach and Boolean logic. Unofficially, we will agreement with puzzles and patterns and advance as abundant mathematics from them as we can. Prerequisites: aerial academy mathematics and alertness to explore. No acclaim in science or engineering. This advance satisfies the Quantitative Acumen requirement.
Engage in lab-based activities advised to strengthen their analytic abilities and aggrandize adeptness of the capacity in accessory mathematics, absorption abnormally on capacity from precalculus and the alteration to calculus. Assay a arrangement of contexts that can be modeled appliance families of functions. Capacity accommodate cone-shaped sections, parametric equations and arctic equations. Multiple representations, transformations, abstracts assay techniques and arrangement amid geometry, anticipation and algebra. Quantitative approaches and architecture relationships amid detached and connected acumen will be alternate themes.
Co-Req: MATH 1320
Presents propositional logic, combinatorics, methods of proof, algebraic systems, algebra of sets, cast algebra, relations and functions, recursion and breeding functions, applications to computer science, and blueprint theory.
Pre-req: MATH 1290 Calculus IB, or MATH 1310 Calculus I, or MATH 1380 Calc. for the Activity Sciences I. or Permission of Instructor/Coordinator or Chair.
Elementary set approach and band-aid sets of systems of beeline equations. An accession to proofs and the absolute methods through a abstraction of the agent amplitude axioms. Beeline analytic geometry. Beeline assurance and independence, subspaces, basis. Close products. Cast algebra. Applications of the aloft will additionally be discussed.
Pre-Req: MATH 1320 Calculus II.
Linear transformations. Beeline operators, change of basis, close artefact and the diagonalization problem. Boxlike forms. Convex sets and geometric programming, input/output models for an economy, Markov chains, added applications of beeline algebra.
Pre-Req: MATH.2210 Beeline Algebra I.
This is a mathematics agreeable advance which covers the geometry/measurement strands of the Massachusetts Class Frameworks in Mathematics at a bookish level. The ambition is not alone to adapt acceptance for the elementary mathematics MTEL, but to lay the accomplishments for alum assignment in elementary mathematics education. The advance centers about “Big Ideas” such as Equivalence, Proportionality, Transformations; and Shapes & Solids. No acclaim in Science or Engineering.
Pre-req: BA-ED Majors only.
Extends the concepts of Calculus I and II that accord with functions of a distinct capricious to multi-variable functions, vector-valued functions and agent fields. Vectors and vector-valued functions, the dot and cantankerous products, curves in amplitude and the calculus of vector-valued functions. Multi-variable functions, limits, continuity, and differentiation. Fractional derivatives, directional derivatives, the gradient, Lagrange multipliers and optimization. Double and amateur integrals in Cartesian, arctic and all-around coordinates. Agent fields and the axiological theorems of agent calculus developed, band and apparent integrals, Green’s theorem, Stokes’s theorem, and the alteration theorem.
Pre-req: MATH.1320 Calculus II, or MATH.2250 Calculus C.
An accession to mathematics accompanying software. Capacity from Calculus & Cogwheel Equations will be explored appliance a allegorical amalgamation like Maple. the advance will additionally acquaint LaTeX, the accepted for book mathematics.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
Topics accommodate methods of solutions for beeline and non-linear aboriginal adjustment cogwheel equations, beeline additional adjustment cogwheel equations, college adjustment beeline cogwheel equations, systems of first-order cogwheel equations. Laplace transforms. Afterwards methods. Applications to concrete systems.
Pre-req: MATH.1320 Calculus II, or MATH.1260 Calculus B.
Introduction to cogwheel equations with an accent on engineering applications. Capacity accommodate first-order equations, higher-order beeline equations with connected coefficients, and systems of first-order equations. Applications of anniversary affair are alien and qualitative, analytical, and afterwards band-aid techniques are studied. Laplace transform methods are discussed. The software amalgamation MATLAB is acclimated throughout the advance for both analytic and afterwards calculations.
Pre-Req: MATH 1320 Calculus II.
Covers the aforementioned capacity as MATH.2310 Calculus II, but in an accomplished environment.
Pre-Req: MATH.1420 Honors Calculus II or permission of instructor
Introduction to cogwheel equations. Capacity accommodate first-order equations, second-order and higher-order beeline equations, systems of first-order beeline equations with connected coefficients, and Laplace transforms.
Pre-Req: MATH 1320 Calculus II.
This advance will acquaint basal programming concepts appliance MATLAB as the programming environment. Capacity accommodate an accession to MATLAB, arrangement manipulation, graphics, calligraphy files, abstracts ascribe and output, relational and analytic operators, codicillary statements, loops, and accepted procedures. Additional capacity will be discussed as time permits. Additional capacity will be called from the following: award roots of nonlinear equations, accidental cardinal generation, Markov processes, simple statistics, interpolation, and the basics of Fourier analysis.
Pre-Req: MATH 1310 Calculus I or MATH 1380 Calculus for Activity Sciences, or Permission of Instructor/Coordinator or Chair.
An accession to anecdotic statistics, graphing and abstracts analysis, anticipation laws, detached and connected anticipation distributions, alternation and regression, amplified statistics. No acclaim in Sciences (except Biology and EEAS) or Engineering. Meets Core Class Essential Learning Outcome for Quantitative Literacy (QL).
This advance provides added apprenticeship in mathematics to acceptance whose Elementary Algebra Accuplacer assay arrangement announce the charge for such instruction. The credits in this advance can not be acclimated to amuse the credits appropriate for graduation, but may be acclimated to amuse the credits appropriate for abounding time apprentice status.
Discusses agent analysis, Green’s Theorem, Alteration Theorem, Stokes’ Theorem, Fourier series, integrals, and fractional cogwheel equations of physics and engineering.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
Introduces acceptance to cast algebra, band-aid of systems of beeline equations, eigenvalues and eigenvectors, band-aid of cogwheel equations by cast methods, alternation band-aid of cogwheel equations, Bessel and Legendre functions, and Sturm-Liouville problems.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
Examines blueprint theory, trees, algebraic systems, Boolean algebra, groups, monoids, automata, machines, rings and fields, applications to coding theory, argumentation design, and sorting.
Pre-req: MATH.2190 Detached Structures I (Formerly MATH.3210), or MATH.3600 Mathematic Structure for Computer Engineers.
This advance will focus on account and autograph mathematics. Acceptance will apprentice how to assay and adapt algebraic statements and accept the acumen abaft these statements. They will additionally apprentice how to back algebraic account and address proofs appliance absolute language, actual logic, and added important elements.
Pre-req: MATH.2190 Detached Structures I.
An accession to allegorical logic. Allegorical argumentation provides a framework of academic acumen with applications in mathematics, cerebral science, computer science and philosophy. Capacity accommodate propositional logic, boolean algebras and rings, first-order argumentation and systems of deduction. Time permitting, we will blow on Tarski’s angle of model, and the abyss and blemish theorems of Godel.
Pre-req: MATH.1310 Calculus I, and MATH.2190 Detached Structures I.
Basic concepts of data. Beeline lists, strings, arrays, and erect lists. Copse and graphs. Storage systems and structures. Storage allocation and collection. Multilinked structures. Symbol tables, analytic and allocation (ordering) techniques. Not for algebraic majors.
Pre-Req: MATH 2310 Calculus III.
Focuses on the approach and appliance of afterwards techniques including absurdity analysis. Additionally discusses band-aid of linear, nonlinear and cogwheel equations, interpolation, afterwards integration, and ambit fitting. Computer solutions are emphasized.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
Computer assay of abstracts acquired from assay conducted in physical, social, and activity sciences. Abstracts preparation. Abstracts modification, book manipulation, and anecdotic statistics appliance SPSS. Programming adeptness is not required. No acclaim in Science or Engineering.
Student works with an adviser to advance a angle for a chief activity that will be agitated out as allotment of MATH.4750 Chief Academy II. Generally taken during the bounce of the inferior year. Prerequisite: Permission of instructor.
Intended for acceptance accepting completed 2 abounding years of physics and math, this advance is advised to advance adequacy in the activated algebraic abilities appropriate of inferior and chief akin physics majors. Covering capacity involving absolute series, adeptness series, circuitous numbers, and beeline algebra forth with agent and Fourier analysis, acceptance will be accomplished with the accuracy appropriate to break a avant-garde ambit of applications in the concrete sciences. Physics majors only.
Pre-req: MATH.2310 Calculus III, and MATH.2340 Cogwheel Equations, or MATH.2360 Engineering Cogwheel Equations, and PHYS.1440 Physics II, or PHYS.1640 Honors Physics II.
Introduction to beginning design, abstracts assay and academic statistical procedures from an activated point of view.
Pre-Req: MATH 1320 Calculus II.
Provides a one-semester advance in anticipation and statistics with applications in the engineering sciences. Anticipation of events, detached and connected accidental variables accumulative distribution, moment generatory functions, chi-square distribution, body functions, distributions. Accession to estimation, antecedent testing, corruption and correlation. No acclaim for both MATH.3860 and MATH.4070, Algebraic majors should booty MATH.4070.
Pre-req: MATH.1320 Calculus II, or MATH.1260 Calculus B.
The complete numbers, completeness, sequences of complete numbers, functions, continuity, compatible continuity, differentiability, the Riemann integral, alternation or complete numbers, sequences and alternation of functions, compatible convergence, adeptness series.
Pre-req: MATH 1320 Calculus II and MATH 3210/2190 Detached Structures I.
Addresses the capacity of probability, accidental variables, detached and connected densities, apprehension and variance, appropriate distributions (binomial, Poisson, normal, etc.), moment breeding functions, collective and codicillary distributions, transformations of variables, sampling, and the axial complete theorem.
Pre-req: MATH 2310 Calculus III, or MATH 2260 Calculus D, and MATH 3210/2190 Detached Structures I. NOTE: No acclaim for both MATH.3860 and MATH.4070.
This advance explores the roles of mainframes, PC’s and duke calculators in instruction, appraise some of the accessible software and accede their use in a arrangement of areas of accessory mathematics, such as algebra, geometry (Euclidean and analytic), anticipation and statistics and anterior calculus. No acclaim in Science or Engineering.
A aboriginal advance in approach of analytic functions of one circuitous variable: circuitous differentiability and the Cauchy-Riemann equations, Cauchy Basal Assumption and Cauchy Basal Formula, Taylor and Laurent series, zeroes of analytic functions and uniqueness, the best modulus principle, abandoned singularities and residues. Applications.
Pre-Req: MATH 2310 Calculus III.
Studies congruencies and the Chinese Remainder Theorem, Primitive roots, boxlike reciprocity, approximation backdrop of connected fractions, Pell’s equation. Recent appliance of cardinal approach such as primality testing, cryptology, and accidental cardinal bearing will additionally be covered.
Pre-req: MATH.2210 Beeline Algebra I, and MATH.2190 Detached Structures I.
A activity -based advance starting with an accession to the basal appearance of Mathematica. A activity that allows the apprentice to focus on assertive appearance in added detail is appropriate and occupies the additional bisected of the course.
Focuses on: algebraic resources, adeptness to use heuristics, the student’s behavior about the use of mathematics to break problems, and the student’s aplomb as a botheration solver. Effective strategies for accumulation botheration analytic in the class will additionally be discussed.
Elementary accumulation theory, groups, cosets, accustomed subgroups, caliber groups, isomorphisms, homomorphisms, applications.
Pre-req: MATH.2190 Detached Structures I.
Metric spaces, topological spaces, connectedness, compactness, the axiological group, classifications of surfaces, Brouwer’s anchored point theorem.
Pre-req: MATH 4030 Algebraic Assay or MATH 5010 Complete Analysis
This advance is advised for accepted and -to-be geometry teachers. In accession to the development of Euclidean geometry, acceptance will become accustomed with geometry applications in Geometer’s Sketchpad software, and to a bottom amount with added geometry software applications including Geogebra, and Cabri. There will be an accession to all-around and abstract geometry and triangle abstracts will be computed for each. Calculus based derivations of breadth and aggregate for surfaces and debris will be generated and accompanying to Euclidean geometry topics.
Pre-Req: MATH 1320 Calculus II.
Examines age-old character systems, Babylonian and Egyptian mathematics, Pythagorean mathematics, duplication, trisection, and quadrature, Euclid’s elements and Greek mathematics afterwards Euclid, Hindu and Arabian mathematics, European mathematics from 500 to 1600, origins of avant-garde mathematics, analytic geometry, the history of calculus. Additionally covers the alteration to the twentieth aeon and abreast perspectives.
Linear and quasilinear aboriginal adjustment PDE. The adjustment of characteristics. Conservation laws and advancement of shocks. Basal approach for three classical equations of algebraic physics (in all spatial dimensions): the beachcomber equation, the heat/diffusion equation, the Laplace/Poisson equation. Initial amount problems – band-aid formulas. Axiological solutions. Green’s functions. Eigenfunction amplification adjustment for initial-boundary and abuttals amount problems.
Pre-Req: MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
Representation of Signals: Fourier analysis, fast Fourier transforms, erect expansions. Transformation of signals: beeline filters, modulation. Band-limited signals. Sampling. Uncertainty principle. Windows and extrapolation. Applications to medical imaging and arrangement processing.
Pre-Reqs: MATH 2310 Calculus III & MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
Applications of mathematics to complete activity problems. Capacity accommodate dimensional analysis, citizenry dynamics beachcomber and calefaction propagation, cartage flow.
Pre-Req: MATH 2340 Cogwheel Equations or MATH 2360 Eng Cogwheel Equations.
An accession to conception and abetment of databases and statistical assay appliance SAS software. SAS is broadly acclimated in the biologic industry, medical assay and added areas. Cannot be acclimated as a Algebraic Elective.
Undergraduate academy on avant-garde algebraic topics. Acceptance are appropriate to advance an compassionate of an avant-garde accountable above the ambit of an absolute advance or amalgamate two or added altered areas anatomy their curriculum. Acceptance are appropriate to participate in the seminar, present their after-effects to the Administration and address a abundant apriorism in their affair area. Essential advance elements accommodate library research, aboriginal research, and both exact and accounting exposition. The aboriginal division is a graduation claim for majors in mathematics.
Pre-Req: MATH.3750 or MATH.4740 Chief Academy I.
An alternative additional division academy to acquiesce for assiduity of abstraction accomplished in Chief Academy I.
Pre-Req: MATH.4750 Chief Academy II.
Point estimation, aplomb intervals, antecedent testing. Two-sample t-test. Alternation and beeline regression. The bivariate accustomed distribution. Assay of about-face for one-and two-way designs. F tests. Nonparametric methods. Chi-squared tests for accident tables. Generalized likelihood ratio. C.R. bound. Consistency.
Pre-req: MATH.4070 Anticipation and Algebraic Statistics I.
Individual abstraction for the apprentice acquisitive added avant-garde or added specialized work. Advance may not be commissioned for appointed offerings. Prerequisite: Permission of Administration Chair.
Individual abstraction for the apprentice acquisitive added avant-garde or added specialized assignment in algebra. May be again for a absolute of six division credits. Advance may not be commissioned for appointed offerings.
Individual abstraction for the apprentice acquisitive added avant-garde or added specialized assignment in Statistics. May be again for a absolute of six division credits. Advance may not be commissioned for appointed offerings. Prerequisite: Permission of Administration Chair.
Unpaid internship in the Administration of Algebraic Sciences. This allows acceptance to accept up to 3 (free elective) credits while alive on an accustomed project. Acceptance who accept a position and who ambition to booty advantage of this Practicum should see the administration Internship Coordinator.
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