Mathematics (MATH)

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Mathematics (MATH) 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
    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.
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  • Newton and Leibniz: the Development of Calculus Isaac Newton (1642-1727)
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  • 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.
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  • The Discovery of the Series Formula for Π by Leibniz, Gregory and Nilakantha Author(S): Ranjan Roy Source: Mathematics Magazine, Vol
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  • 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.
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  • Mathematics: the Science of Patterns
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  • History of Mathematics
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  • 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.
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  • 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.
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  • Lecture 1: Mathematical Roots
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  • MATH 531.01: Topology
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