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Course Descriptions MATH 1080 QL MATH 1210 QL Mathematics (MATH) Precalculus Calculus I 5 5 MATH 100R * Prerequisite(s): Within the past two years, * Prerequisite(s): One of the following within Math Leap one of the following: MAT 1000 or MAT 1010 the past two years: (MATH 1050 or MATH 1 with a grade of B or better or an appropriate 1055) and MATH 1060, each with a grade of Is part of UVU’s math placement process; for math placement score. C or higher; OR MATH 1080 with a grade of C students who desire to review math topics Is an accelerated version of MATH 1050 or higher; OR appropriate placement by math in order to improve placement level before and MATH 1060. Includes functions and placement test. beginning a math course. Addresses unique their graphs including polynomial, rational, Covers limits, continuity, differentiation, strengths and weaknesses of students, by exponential, logarithmic, trigonometric, and applications of differentiation, integration, providing group problem solving activities along inverse trigonometric functions. Covers and applications of integration, including with an individual assessment and study inequalities, systems of linear and derivatives and integrals of polynomial plan for mastering target material. Requires nonlinear equations, matrices, determinants, functions, rational functions, exponential mandatory class attendance and a minimum arithmetic and geometric sequences, the functions, logarithmic functions, trigonometric number of hours per week logged into a Binomial Theorem, the unit circle, right functions, inverse trigonometric functions, and preparation module, with progress monitored triangle trigonometry, trigonometric equations, hyperbolic functions. Is a prerequisite for by a mentor. May be repeated for a maximum trigonometric identities, the Law of Sines, the calculus-based sciences. of 4 credits toward graduation. May be graded Law of Cosines, vectors, complex numbers, credit/no credit. polar coordinates, and conic sections. MATH 121H QL Calculus I MATH 1050 QL MATH 1090 QL 5 College Algebra College Algebra for Business * Prerequisite(s): One of the following within 4 3 the past two years: (MATH 1050 or MATH * Prerequisite(s): Within the past two years * Prerequisite(s): Within the past two years 1055) and MATH 1060, each with a grade of one of the following: MAT 1000 or MAT 1010 one of the following: MAT 1000 or MAT 1010 C or higher; OR MATH 1080 with a grade of C with a grade of C or better or appropriate math with a grade of C or better or appropriate math or higher; OR appropriate placement by math placement score. placement score. placement test. Includes inequalities, functions and their Uses linear, quadratic, power, polynomial, Covers limits, continuity, differentiation, graphs, polynomial and rational functions, rational, exponential, logarithmic, and logistic applications of differentiation, integration, exponential and logarithmic functions, systems functions to analyze business applications and applications of integration, including of linear and nonlinear equations, matrices such as market equilibrium, rates of derivatives and integrals of polynomial and determinants, arithmetic and geometric change, cost-benefit analysis, and inflation. functions, rational functions, exponential sequences, and the Binomial Theorem. May be Includes systems of linear and non-linear functions, logarithmic functions, trigonometric delivered hybrid and/or online. equations and inequalities, matrices and functions, inverse trigonometric functions, and matrix equations, sequences and series, and hyperbolic functions. Is a prerequisite for MATH 1055 QL financial mathematics. Canvas Course Mats calculus-based sciences. Is an honors course College Algebra with Preliminaries $90/McGraw applies. with student projects. 5 * Prerequisite(s): Within the past two years MATH 1100 QL MATH 1220 one of the following: MAT 1000 or MAT 1010 Introduction to Calculus Calculus II with a grade of C or better or appropriate math 4 5 placement score. * Prerequisite(s): Within the past two years: * Prerequisite(s): MATH 1210 or MATH 121H Includes inequalities, functions and their MATH 1050 or MATH 1055 or MATH 1080 with a grade of C or higher graphs, polynomial and rational functions, with a grade of C or better or appropriate math Includes integration techniques, arc length, exponential and logarithmic functions, systems placement score. area of a surface of revolution, moments of linear and nonlinear equations, matrices Provides an overview of the basic concepts and centers of mass, sequences and and determinants, arithmetic and geometric and techniques of differential and integral series, parametrization of curves and polar sequences, and the Binomial Theorem. May calculus. Features applications in business, coordinates, vectors in 3-space, and quadric be delivered hybrid and/or online. Lab access economics, and the life, social, and physical surfaces. fee of $30 applies. Canvas Course Mats $90/ sciences. Includes optimization techniques in McGraw applies. multivariable differential calculus. MATH 122H Calculus II MATH 1060 5 Trigonometry * Prerequisite(s): MATH 1210 or MATH 121H 3 with a grade of C or higher * Prerequisite(s): Within the past two years: MATH 1050 or MATH 1055 with a grade of Includes integration techniques, arc length, C or higher or appropriate math placement area of a surface of revolution, moments score. and centers of mass, sequences and series, parametrization of curves and polar Includes the unit circle and right triangle coordinates, vectors in 3-space, and quadric definitions of the trigonometric functions, surfaces. Honors course which requires a graphing trigonometric functions, trigonometric student project. identities, trigonometric equations, inverse trigonometric functions, the Law of Sines and the Law of Cosines, vectors, complex numbers, polar coordinates, and rotation of axes. Utah Valley University Course Catalog 2021-2022 1 Course Descriptions MATH 2000 QL MATH 2250 MATH 3000 Algebraic Reasoning with Modeling Differential Equations and Linear Algebra History of Mathematics WE 3 4 3 * Prerequisite(s): Within the past two years, * Prerequisite(s): MATH 1220 or MATH 122H * Prerequisite(s): MATH 2210 or MATH 221H one of the following: MAT 1000 or MAT 1010 with a grade of C or higher with a grade of C or higher and University with a grade of C or better or an appropriate Is for engineering students. Includes separable Advanced Standing math placement score. equations, linear differential equations, Provides a survey of the history of mathematics Presents the basic ideas of sets and functions differential operators and annihilators, variation with a focus on the development of in the context of and motivated by modeling of parameters, Laplace transforms, and mathematical ideas in their historical context. bivariate data. Includes basic set theory such systems of linear differential equations. Includes numeration systems, the mathematics as unions, intersections, Venn diagrams, etc. Introduces basic concepts of linear algebra of the ancient world, the development of Includes the basic ideas and the algebra including matrices, Gaussian elimination, algebra, geometry, and calculus, and the work of functions including polynomial, exponential, determinants, linear independence, and of pivotal mathematicians. and logarithmic functions. Also includes some eigenvalues and eigenvectors. basic combinatorics and counting principles as MATH 3010 well as arithmetic and geometric sequences. MATH 2270 Methods of Secondary School Mathematics Culminates in a pictorial introduction to the Linear Algebra Teaching basic ideas of calculus presented with minimal 3 3 computation. * Prerequisite(s): MATH 1220 or MATH 122H * Prerequisite(s): MATH 2210 or MATH 221H with a grade of C or higher with a grade of C or higher and EDSC 455G MATH 2010 with a grade of B- or higher and University Includes matrices and systems of Advanced Standing Mathematics for Elementary Teachers I equations, determinants, vector spaces, linear 3 transformations, orthogonality, and eigenvalues Is for Mathematics Education majors. Presents * Prerequisite(s): Within the past two years: and eigenvectors. different methods of teaching mathematical MATH 1050 or MATH 1055 or MATH 2000 ideas at the secondary school level. Includes with a grade of C or better or appropriate math MATH 2280 classroom instruction, student presentations, placement score. Ordinary Differential Equations and field experiences. Studies various Is for pre-elementary education majors. 3 techniques of assessment and classroom Includes problem solving, sets, numeration * Prerequisite(s): MATH 2210 or MATH 221H management. systems, arithmetic of whole numbers, integers, with a grade of C or higher MATH 3020 rational numbers, real numbers, elementary Includes separable equations, linear number theory, ratios, proportions, decimals, differential equations, differential operators Computer Based Mathematics for and percents. and annihilators, variation of parameters, Secondary School Mathematics Teachers power series solutions of differential equations, 3 MATH 2020 * Prerequisite(s): (MATH 2210 and MATH Laplace transforms, systems of linear Mathematics for Elementary Teachers II 2270 each with a grade of C or higher) and differential equations, and numerical methods. 3 University Advanced Standing; MATH 2280 * Prerequisite(s): MATH 2010 with a grade of MATH 281R with a grade of C or higher is recommended C or higher Cooperative Work Experience For Mathematics
Recommended publications
  • An Appreciation of Euler's Formula

    An Appreciation of Euler's Formula

    Rose-Hulman Undergraduate Mathematics Journal Volume 18 Issue 1 Article 17 An Appreciation of Euler's Formula Caleb Larson North Dakota State University Follow this and additional works at: https://scholar.rose-hulman.edu/rhumj Recommended Citation Larson, Caleb (2017) "An Appreciation of Euler's Formula," Rose-Hulman Undergraduate Mathematics Journal: Vol. 18 : Iss. 1 , Article 17. Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/17 Rose- Hulman Undergraduate Mathematics Journal an appreciation of euler's formula Caleb Larson a Volume 18, No. 1, Spring 2017 Sponsored by Rose-Hulman Institute of Technology Department of Mathematics Terre Haute, IN 47803 [email protected] a scholar.rose-hulman.edu/rhumj North Dakota State University Rose-Hulman Undergraduate Mathematics Journal Volume 18, No. 1, Spring 2017 an appreciation of euler's formula Caleb Larson Abstract. For many mathematicians, a certain characteristic about an area of mathematics will lure him/her to study that area further. That characteristic might be an interesting conclusion, an intricate implication, or an appreciation of the impact that the area has upon mathematics. The particular area that we will be exploring is Euler's Formula, eix = cos x + i sin x, and as a result, Euler's Identity, eiπ + 1 = 0. Throughout this paper, we will develop an appreciation for Euler's Formula as it combines the seemingly unrelated exponential functions, imaginary numbers, and trigonometric functions into a single formula. To appreciate and further understand Euler's Formula, we will give attention to the individual aspects of the formula, and develop the necessary tools to prove it.
  • Newton and Leibniz: the Development of Calculus Isaac Newton (1642-1727)

    Newton and Leibniz: the Development of Calculus Isaac Newton (1642-1727)

    Newton and Leibniz: The development of calculus Isaac Newton (1642-1727) Isaac Newton was born on Christmas day in 1642, the same year that Galileo died. This coincidence seemed to be symbolic and in many ways, Newton developed both mathematics and physics from where Galileo had left off. A few months before his birth, his father died and his mother had remarried and Isaac was raised by his grandmother. His uncle recognized Newton’s mathematical abilities and suggested he enroll in Trinity College in Cambridge. Newton at Trinity College At Trinity, Newton keenly studied Euclid, Descartes, Kepler, Galileo, Viete and Wallis. He wrote later to Robert Hooke, “If I have seen farther, it is because I have stood on the shoulders of giants.” Shortly after he received his Bachelor’s degree in 1665, Cambridge University was closed due to the bubonic plague and so he went to his grandmother’s house where he dived deep into his mathematics and physics without interruption. During this time, he made four major discoveries: (a) the binomial theorem; (b) calculus ; (c) the law of universal gravitation and (d) the nature of light. The binomial theorem, as we discussed, was of course known to the Chinese, the Indians, and was re-discovered by Blaise Pascal. But Newton’s innovation is to discuss it for fractional powers. The binomial theorem Newton’s notation in many places is a bit clumsy and he would write his version of the binomial theorem as: In modern notation, the left hand side is (P+PQ)m/n and the first term on the right hand side is Pm/n and the other terms are: The binomial theorem as a Taylor series What we see here is the Taylor series expansion of the function (1+Q)m/n.
  • Mathematics 1

    Mathematics 1

    Mathematics 1 Mathematics Department Information • Department Chair: Friedrich Littmann, Ph.D. • Graduate Coordinator: Indranil Sengupta, Ph.D. • Department Location: 412 Minard Hall • Department Phone: (701) 231-8171 • Department Web Site: www.ndsu.edu/math (http://www.ndsu.edu/math/) • Application Deadline: March 1 to be considered for assistantships for fall. Openings may be very limited for spring. • Credential Offered: Ph.D., M.S. • English Proficiency Requirements: TOEFL iBT 71; IELTS 6 Program Description The Department of Mathematics offers graduate study leading to the degrees of Master of Science (M.S.) and Doctor of Philosophy (Ph.D.). Advanced work may be specialized among the following areas: • algebra, including algebraic number theory, commutative algebra, and homological algebra • analysis, including analytic number theory, approximation theory, ergodic theory, harmonic analysis, and operator algebras • applied mathematics, mathematical finance, mathematical biology, differential equations, dynamical systems, • combinatorics and graph theory • geometry/topology, including differential geometry, geometric group theory, and symplectic topology Beginning with their first year in residence, students are strongly urged to attend research seminars and discuss research opportunities with faculty members. By the end of their second semester, students select an advisory committee and develop a plan of study specifying how all degree requirements are to be met. One philosophical tenet of the Department of Mathematics graduate program is that each mathematics graduate student will be well grounded in at least two foundational areas of mathematics. To this end, each student's background will be assessed, and the student will be directed to the appropriate level of study. The Department of Mathematics graduate program is open to all qualified graduates of universities and colleges of recognized standing.
  • The Discovery of the Series Formula for Π by Leibniz, Gregory and Nilakantha Author(S): Ranjan Roy Source: Mathematics Magazine, Vol

    The Discovery of the Series Formula for Π by Leibniz, Gregory and Nilakantha Author(S): Ranjan Roy Source: Mathematics Magazine, Vol

    The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha Author(s): Ranjan Roy Source: Mathematics Magazine, Vol. 63, No. 5 (Dec., 1990), pp. 291-306 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/2690896 Accessed: 27-02-2017 22:02 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to Mathematics Magazine This content downloaded from 195.251.161.31 on Mon, 27 Feb 2017 22:02:42 UTC All use subject to http://about.jstor.org/terms ARTICLES The Discovery of the Series Formula for 7r by Leibniz, Gregory and Nilakantha RANJAN ROY Beloit College Beloit, WI 53511 1. Introduction The formula for -r mentioned in the title of this article is 4 3 57 . (1) One simple and well-known moderm proof goes as follows: x I arctan x = | 1 +2 dt x3 +5 - +2n + 1 x t2n+2 + -w3 - +(-I)rl2n+1 +(-I)l?lf dt. The last integral tends to zero if Ix < 1, for 'o t+2dt < jt dt - iX2n+3 20 as n oo.
  • 1. More Examples Example 1. Find the Slope of the Tangent Line at (3,9)

    1. More Examples Example 1. Find the Slope of the Tangent Line at (3,9)

    1. More examples Example 1. Find the slope of the tangent line at (3; 9) to the curve y = x2. P = (3; 9). So Q = (3 + ∆x; 9 + ∆y). 9 + ∆y = (3 + ∆x)2 = (9 + 6∆x + (∆x)2. Thus, we have ∆y = 6 + ∆x. ∆x If we let ∆ go to zero, we get ∆y lim = 6 + 0 = 6. ∆x→0 ∆x Thus, the slope of the tangent line at (3; 9) is 6. Let's consider a more abstract example. Example 2. Find the slope of the tangent line at an arbitrary point P = (x; y) on the curve y = x2. Again, P = (x; y), and Q = (x + ∆x; y + ∆y), where y + ∆y = (x + ∆x)2 = x2 + 2x∆x + (∆x)2. So we get, ∆y = 2x + ∆x. ∆x Letting ∆x go to zero, we get ∆y lim = 2x + 0 = 2x. ∆x→0 ∆x Thus, the slope of the tangent line at an arbitrary point (x; y) is 2x. Example 3. Find the slope of the tangent line at an arbitrary point P = (x; y) on the curve y = ax3, where a is a real number. Q = (x + ∆x; y + ∆y). We get, 1 2 y + ∆y = a(x + ∆x)3 = a(x3 + 3x2∆x + 3x(∆x)2 + (∆x)3). After simplifying we have, ∆y = 3ax2 + 3xa∆x + a(∆x)2. ∆x Letting ∆x go to 0 we conclude, ∆y 2 2 mP = lim = 3ax + 0 + 0 = 3ax . x→0 ∆x 2 Thus, the slope of the tangent line at a point (x; y) is mP = 3ax . Example 4.
  • Mathematics: the Science of Patterns

    Mathematics: the Science of Patterns

    _RE The Science of Patterns LYNNARTHUR STEEN forcesoutside mathematics while contributingto humancivilization The rapid growth of computing and applicationshas a rich and ever-changingvariety of intellectualflora and fauna. helpedcross-fertilize the mathematicalsciences, yielding These differencesin perceptionare due primarilyto the steep and an unprecedentedabundance of new methods,theories, harshterrain of abstractlanguage that separatesthe mathematical andmodels. Examples from statisiicalscienceX core math- rainforest from the domainof ordinaryhuman activity. ematics,and applied mathematics illustrate these changes, The densejungle of mathematicshas beennourished for millennia which have both broadenedand enrichedthe relation by challengesof practicalapplications. In recentyears, computers between mathematicsand science. No longer just the have amplifiedthe impact of applications;together, computation study of number and space, mathematicalscience has and applicationshave swept like a cyclone across the terrainof become the science of patterlls, with theory built on mathematics.Forces -unleashed by the interactionof theseintellectu- relations among patterns and on applicationsderived al stormshave changed forever and for the better the morpholo- from the fit betweenpattern and observation. gy of mathematics.In their wake have emergednew openingsthat link diverseparts of the mathematicalforest, making possible cross- fertilizationof isolatedparts that has immeasurablystrengthened the whole. MODERN MATHEMATICSJUST MARKED ITS 300TH BIRTH-
  • History of Mathematics

    History of Mathematics

    History of Mathematics James Tattersall, Providence College (Chair) Janet Beery, University of Redlands Robert E. Bradley, Adelphi University V. Frederick Rickey, United States Military Academy Lawrence Shirley, Towson University Introduction. There are many excellent reasons to study the history of mathematics. It helps students develop a deeper understanding of the mathematics they have already studied by seeing how it was developed over time and in various places. It encourages creative and flexible thinking by allowing students to see historical evidence that there are different and perfectly valid ways to view concepts and to carry out computations. Ideally, a History of Mathematics course should be a part of every mathematics major program. A course taught at the sophomore-level allows mathematics students to see the great wealth of mathematics that lies before them and encourages them to continue studying the subject. A one- or two-semester course taught at the senior level can dig deeper into the history of mathematics, incorporating many ideas from the 19th and 20th centuries that could only be approached with difficulty by less prepared students. Such a senior-level course might be a capstone experience taught in a seminar format. It would be wonderful for students, especially those planning to become middle school or high school mathematics teachers, to have the opportunity to take advantage of both options. We also encourage History of Mathematics courses taught to entering students interested in mathematics, perhaps as First Year or Honors Seminars; to general education students at any level; and to junior and senior mathematics majors and minors. Ideally, mathematics history would be incorporated seamlessly into all courses in the undergraduate mathematics curriculum in addition to being addressed in a few courses of the type we have listed.
  • Leonhard Euler: His Life, the Man, and His Works∗

    Leonhard Euler: His Life, the Man, and His Works∗

    SIAM REVIEW c 2008 Walter Gautschi Vol. 50, No. 1, pp. 3–33 Leonhard Euler: His Life, the Man, and His Works∗ Walter Gautschi† Abstract. On the occasion of the 300th anniversary (on April 15, 2007) of Euler’s birth, an attempt is made to bring Euler’s genius to the attention of a broad segment of the educated public. The three stations of his life—Basel, St. Petersburg, andBerlin—are sketchedandthe principal works identified in more or less chronological order. To convey a flavor of his work andits impact on modernscience, a few of Euler’s memorable contributions are selected anddiscussedinmore detail. Remarks on Euler’s personality, intellect, andcraftsmanship roundout the presentation. Key words. LeonhardEuler, sketch of Euler’s life, works, andpersonality AMS subject classification. 01A50 DOI. 10.1137/070702710 Seh ich die Werke der Meister an, So sehe ich, was sie getan; Betracht ich meine Siebensachen, Seh ich, was ich h¨att sollen machen. –Goethe, Weimar 1814/1815 1. Introduction. It is a virtually impossible task to do justice, in a short span of time and space, to the great genius of Leonhard Euler. All we can do, in this lecture, is to bring across some glimpses of Euler’s incredibly voluminous and diverse work, which today fills 74 massive volumes of the Opera omnia (with two more to come). Nine additional volumes of correspondence are planned and have already appeared in part, and about seven volumes of notebooks and diaries still await editing! We begin in section 2 with a brief outline of Euler’s life, going through the three stations of his life: Basel, St.
  • History and Pedagogy of Mathematics in Mathematics Education: History of the Field, the Potential of Current Examples, and Directions for the Future Kathleen Clark

    History and Pedagogy of Mathematics in Mathematics Education: History of the Field, the Potential of Current Examples, and Directions for the Future Kathleen Clark

    History and pedagogy of mathematics in mathematics education: History of the field, the potential of current examples, and directions for the future Kathleen Clark To cite this version: Kathleen Clark. History and pedagogy of mathematics in mathematics education: History of the field, the potential of current examples, and directions for the future. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. hal-02436281 HAL Id: hal-02436281 https://hal.archives-ouvertes.fr/hal-02436281 Submitted on 12 Jan 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. History and pedagogy of mathematics in mathematics education: History of the field, the potential of current examples, and directions for the future Kathleen M. Clark Florida State University, School of Teacher Education, Tallahassee, Florida USA; [email protected] The field of history of mathematics in mathematics education—often referred to as the history and pedagogy of mathematics domain (or, HPM domain)—can be characterized by an interesting and rich past and a vibrant and promising future. In this plenary, I describe highlights from the development of the field, and in doing so, I focus on several ways in which research in the field of history of mathematics in mathematics education offers important connections to frameworks and areas of long-standing interest within mathematics education research, with a particular emphasis on student learning.
  • Lecture 1: Mathematical Roots

    Lecture 1: Mathematical Roots

    E-320: Teaching Math with a Historical Perspective O. Knill, 2010-2017 Lecture 1: Mathematical roots Similarly, as one has distinguished the canons of rhetorics: memory, invention, delivery, style, and arrangement, or combined the trivium: grammar, logic and rhetorics, with the quadrivium: arithmetic, geometry, music, and astronomy, to obtain the seven liberal arts and sciences, one has tried to organize all mathematical activities. counting and sorting arithmetic Historically, one has dis- spacing and distancing geometry tinguished eight ancient positioning and locating topology roots of mathematics. surveying and angulating trigonometry Each of these 8 activities in balancing and weighing statics turn suggest a key area in moving and hitting dynamics mathematics: guessing and judging probability collecting and ordering algorithms To morph these 8 roots to the 12 mathematical areas covered in this class, we complemented the ancient roots with calculus, numerics and computer science, merge trigonometry with geometry, separate arithmetic into number theory, algebra and arithmetic and turn statics into analysis. counting and sorting arithmetic spacing and distancing geometry positioning and locating topology Lets call this modern adap- dividing and comparing number theory tation the balancing and weighing analysis moving and hitting dynamics 12 modern roots of guessing and judging probability Mathematics: collecting and ordering algorithms slicing and stacking calculus operating and memorizing computer science optimizing and planning numerics manipulating and solving algebra Arithmetic numbers and number systems Geometry invariance, symmetries, measurement, maps While relating math- Number theory Diophantine equations, factorizations ematical areas with Algebra algebraic and discrete structures human activities is Calculus limits, derivatives, integrals useful, it makes sense Set Theory set theory, foundations and formalisms to select specific top- Probability combinatorics, measure theory and statistics ics in each of this area.
  • MATH 531.01: Topology

    MATH 531.01: Topology

    University of Montana ScholarWorks at University of Montana Syllabi Course Syllabi Fall 9-1-2000 MATH 531.01: Topology Karel M. Stroethoff University of Montana, Missoula, [email protected] Follow this and additional works at: https://scholarworks.umt.edu/syllabi Let us know how access to this document benefits ou.y Recommended Citation Stroethoff, Karel M., "MATH 531.01: Topology" (2000). Syllabi. 5961. https://scholarworks.umt.edu/syllabi/5961 This Syllabus is brought to you for free and open access by the Course Syllabi at ScholarWorks at University of Montana. It has been accepted for inclusion in Syllabi by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact [email protected]. M ath 531 — Topology Fall Semester 2000 Class: MWF: 11:10 pm - 12:00 noon; MA 211; CRN: 73628 Class website: http://www.math.umt.edu/~stroet/531.htinl Instructor: Karel Stroethoff Contact Coordinates: Office: MA 309 Phone: 243-4082 or 243-5311 (secretaries) E-mail: [email protected] Homepage: h ttp ://www.math.umt.edu/~stroet/ Office H ours: See webpage. Description: One of the most important developments in twentieth century mathematics has been the formation of topology as an independent field of study and the systematic application of topological ideas to other fields of mathematics. The beginnings of algebraic and geometric topology can be traced, to the results of Leonhard Euler (1707-1783) on polyhedra and graph theory. Point-set topology or general topology has its origin in nine­ teenthcentury works establishing a rigorous basis for the Calculus. Currently topological ideas are prevalent in many areas of mathematics, not only in pure subject areas, but even in the most applied fields.
  • Mathematics (MATH) 1

    Mathematics (MATH) 1

    Mathematics (MATH) 1 MATHEMATICS (MATH) MATH 1000 Special Problems (IND 0.0-6.0) MATH 1208 Calculus With Analytic Geometry I (LEC 5.0) Problems or readings in specific subjects or projects in the department. A study of limits, continuity, differentiation and integration of algebraic Consent of instructor required. and trigonometric functions. Applications of these concepts in physical as well as mathematical settings are considered. Credit will only be given MATH 1001 Special Topics (LAB 0.0 and LEC 0.0) for one of Math 1208 or Math 1214. Prerequisites: Math 1160; Math 1120 or 1140, both with a grade of "C"; or better; or by placement exam. This course is designed to give the department an opportunity to test a new course. Variable title. MATH 1210 Calculus I-A (LAB 1.0 and LEC 3.0) MATH 1101 Introduction To Mathematics (LEC 1.0) An introduction to differential and integral calculus for students Introduction to the department, program of study, methods of study, and needing extra algebra or trigonometry content. Emphasizes differential an introduction of the various areas of mathematics. Required of fall calculus along with linear, polynomial, rational, and radical functions semester freshman mathematics majors. and equations. Math 1210 and 1211 combined cover the same calculus content as Math 1214. Credit will be given for only one of Math 1210 or Math 1214. Prerequisites: A grade of "C" or better in either Math 1120 or MATH 1103 Fundamentals Of Algebra (LEC 3.0) Math 1140, or by placement exam. Basic principles of algebra including the number line and an introduction to equations and inequalities, polynomials, rational expressions, exponents and radicals, the quadratic formula and functions.