Download e-book Lectures on Analysis II. Math 502 with homeworks

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How should I plan for a math major? Take a look at the math major requirements. You'll need: three calculus courses and a freshman seminar; the algebra and analysis sequences; complex analysis and PDE; and electives. Most math elective courses have particular prerequisites--think about not only which courses you'll take, but also what order you'll take them in!

I've provided some sample major plans to the right. What can I expect as a math major? In the lower division classes e. Familiarity with computation and these basic objects is the base upon which much of the upper-division coursework builds. In some upper-division classes, you'll learn to abstract the essential features of the objects you learned about in the calculus sequence.

Topics addressed in these courses include fundamental questions like What is a number? In these courses, students investigate reasons behind the theorems of the calculus sequence, as well as generalizing those theorems to broader contexts. Other upper-division courses will introduce branches of mathematics you may not have previously encountered, such as combinatorics, number theory, differential geometry, topology, and game theory.

Generally, for major courses, you can expect to spend at least 15 hours outside of class on homework and required reading. Of course this is only an estimate. Depending on the particular course, instructor, and student, you may need to spend more or less time outside of class. What is Honors Calculus? The Honors Calculus sequence MATH is a two-semester course which covers multivariable calculus, differential equations, and some linear algebra.

Effective Fall , all Applied Mathematics and Pure Mathematics courses have been renamed as Mathematics with a change in course number in some cases. Please refer to the descriptions of the individual Mathematics courses for details. Students enrolled in any program that requires any Applied Mathematics or Pure Mathematics course should use the corresponding Mathematics course as replacement.


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Course Hours: 0. Notes: This course covers topics to allow students with credit in Mathematics to be permitted to register in Mathematics Junior Courses. Topics selected by the instructor to provide a contemporary mathematical perspective and experiences in mathematical thinking. May include historical material on the development of classical mathematical ideas as well as the evolution of recent mathematics. Notes: Not included in the Field of Mathematics.


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Geometrical applications and computing techniques will be emphasized. Students will complete a project using mathematical software. Additional topics include linear transformations, determinants, complex numbers, eigenvalues, and applications. Antirequisite s : Credit for Mathematics and will not be allowed.

Topics include fields, subspaces, bases and dimension, linear transformations, determinants, eigenvalues and eigenvectors. Course Hours: 3 units; Prerequisite s : A grade of 80 per cent or higher in Mathematics Limits, derivatives and integrals of algebraic, exponential, logarithmic and trigonometric functions play a central role. Additional topics include applications of differentiation; the fundamental theorem of calculus, improper integrals and applications of integration.

Antirequisite s : Not open to students with 50 per cent or higher in Mathematics 31 or a grade of "C" or higher in Mathematics 3 offered through University of Calgary Continuing Education, except with special departmental permission.

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Credit for Mathematics and either or will not be allowed. Limits, derivatives, and integrals of algebraic, exponential, logarithmic and trigonometric functions play a central role. Differential calculus in several variables will also be introduced. Antirequisite s : Credit for Mathematics and either or will not be allowed.

Single variable calculus: techniques of integration, sequences, series, convergence tests, and Taylor series. Calculus of several variables: partial differentiation, multiple integration, parametric equations, and applications Course Hours: 3 units; Prerequisite s : One of Mathematics , or Course Hours: 3 units; T-1 Prerequisite s : Mathematics or Topics include functions, sets and relations; the integers, prime numbers, divisibility and modular arithmetic; induction and recursion; real numbers; Cauchy sequences and completeness; complex numbers.

Differentiation: derivative laws, the mean value theorem, optimization, curve sketching and other applications. Integral calculus: the fundamental theorem of calculus, techniques of integration, improper integrals, and areas of planar regions. Course Hours: 3 units; T Senior Courses. Course Hours: 3 units; T Prerequisite s : Mathematics or ; and or This course is not in the field of Mathematics.

Also known as: Education back to top. Course Hours: 3 units; T Prerequisite s : Mathematics Also known as: formerly Mathematics back to top. Course Hours: 3 units; T Prerequisite s : Mathematics or Rings and fields: the integers modulo n, polynomial rings, ring homomorphisms, ideals, quotient rings the isomorphism theorem, unique factorization domains, principal ideal domains, Euclidean domains and the construction of finite fields.

Antirequisite s : Credit for Mathematics and Pure Mathematics will not be allowed. Also known as: formerly Pure Mathematics back to top. Symmetric and public-key cryptosystems; one-way and trapdoor functions; mechanisms for data integrity; digital signatures; key management; applications to the design of cryptographic systems. Assessment will primarily focus on mathematical theory and proof-oriented homework problems; additional application programming exercises will be available for extra credit. Course Hours: 3 units; Prerequisite s : Mathematics or Antirequisite s : Credit for Mathematics and any of Pure Mathematics , Computer Science , , or will not be allowed.

Course Hours: 3 units; T Prerequisite s : Mathematics or ; and one other level course from the Field of Mathematics. The theory of curves studies global properties of curves such as the four vertex theorem. The theory of surfaces introduces the fundamental quadratic forms of a surface, intrinsic and extrinsic geometry of surfaces, and the Gauss-Bonnet theorem.

Course Hours: 3 units; Prerequisite s : Mathematics or ; Mathematics or ; Mathematics or Course Hours: 3 units; T Prerequisite s : Mathematics or ; one of Mathematics , or Also known as: formerly Applied Mathematics back to top. Differential equations: linear ordinary differential equations, and systems of ordinary differential equations. Calculus of several variables: partial differentiation, the chain rule, double and triple integrals. Introduction to vector analysis: theorems of Green, Gauss and Stokes.

Additional topics: notions of probability and normal distribution; the Fourier transform. Notes: This course is not part of the Field of Mathematics. Mathematics will contain more challenging and deeper assessment than Mathematics Inner product spaces, invariant subspaces and spectral theory. Quadratic forms. Functions of several variables; limits, continuity, differentiability, partial differentiation, applications including optimization and Lagrange multipliers.

Course Hours: 3 units; Prerequisite s : Mathematics or ; and one of Mathematics , or Course Hours: 3 units; Antirequisite s : Credit for Mathematics and either or Applied Mathematics will not be allowed. Antirequisite s : Credit for Mathematics and or Applied Mathematics will not be allowed. Topics include: risk, return, no arbitrage principle; basic financial derivatives: options, forwards and future contracts; risk free assets, time value of money, zero coupon bonds; risky assets, binomial tree model, fundamental theorem of asset pricing; portfolio management and capital asset pricing model; no arbitrage pricing of financial derivatives; hedging.

Course Hours: 3 units; T Prerequisite s : Statistics Antirequisite s : Credit for Mathematics and Computer Science will not be allowed. Course Hours: 3 units; Prerequisite s : Consent of the Department. Multiple integrals. Analysis of functions. Compact sets. Convex sets. Separating hyperplanes. Lower and upper hemi-continuous correspondences. Fixed point theorems, Optimal control. Course Hours: 3 units; Prerequisite s : Mathematics or ; Mathematics or or both Economics and Course Hours: 3 units; T Prerequisite s : One of Mathematics , , or Applied Mathematics ; and Mathematics or or Also known as: formerly Applied Mathematics back to top.

Fourier and Laplace transforms, applications and numerical methods. Functions of a complex variable and applications. Designing and attacking public key cryptosystems based on number theory. Basic techniques for primality testing, factoring and extracting discrete logarithms. Elliptic curve cryptography. Additional topics may include knapsack systems, zero knowledge, attacks on hash functions, identity-based cryptography, and quantum cryptography.

Group theory: group actions, Sylow theorems, solvable, nilpotent and p-groups, simplicity of alternating groups and PSL n,q.

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Field theory: algebraic and transcendental extensions, separability and normality, Galois theory, insolvability of the general quintic equation, and computation of Galois groups over the rationals. Course Hours: 3 units; Prerequisite s : Mathematics or ; one of Mathematics , Pure Mathematics or Laplace Transforms. Partial differential equations. Complex analysis. Residue integrals. Extensive physical applications. Course Hours: 3 units; Prerequisite s : Mathematics or ; one of Mathematics , , or ; Mathematics or Antirequisite s : Credit for Mathematics and either Mathematics or Pure Mathematics will not be allowed.

Course Hours: 3 units; Prerequisite s : Mathematics or ; and 3 units of Mathematics in the Field of Mathematics at the level or higher. Antirequisite s : Credit for Mathematics and any one of Mathematics , Pure Mathematics or will not be allowed. Course Hours: 3 units; Prerequisite s : Any two Mathematics courses in the Field of Mathematics at the level or above.

Course Hours: 3 units; Prerequisite s : Mathematics or ; and one of Mathematics , or Applied Mathematics Major topics include: snake lemma; free modules; tensor product; hom-tensor duality; finitely presented modules; invariant factors; free resolutions; and the classification of finitely generated modules over principal ideal domains.

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Adjoint functors play a large role. The course includes applications to linear algebra, including rational forms.

Course Hours: 3 units; Prerequisite s : Mathematics , or ; Mathematics or Pure Mathematics ; 3 units of Mathematics in the Field of Mathematics at the level or higher. Antirequisite s : Credit for Mathematics and either or Pure Mathematics will not be allowed. Topics covered will vary based on interests of students and instructor. Course Hours: 3 units; Prerequisite s : Mathematics or Pure Mathematics ; 3 units of Mathematics from the Field of Mathematics at the level or above. Students will investigate scientific or social issues by applying mathematical methods acquired in previous mathematics courses.

A final project will be submitted at the end of the term and its contents summarized in a presentation. Course Hours: 3 units; 1. Students will produce and present a substantial thesis under the supervision of a faculty member. The emphasis is on how to address theoretical or real world scientific or social issues by applying the various mathematical methods acquired in the earlier years in a unified and appropriate way. Notes: This course extends over the Fall and Winter Terms. Students will meet regularly with their thesis supervisors during the terms.

Students submit a thesis, and the course culminates in a series of student presentations. A grade of "B" or higher is required for the Honours program. Students are advised to consult with the Undergraduate Director for information and advice before registration into the course. Students earning an Honours degree in Mathematics along with a concentration in Statistics must complete both Mathematics and Statistics Holomorphic function, Cauchy integral formula and its applications. Yes, we require a placement test for all of our students. A student needs to be registered in the same way as our regular students; registration fee applies.

It is difficult for most home schooling families to commit to educational classes on weekends since weekends. Can you schedule more classes during the day on week days? We will be glad to add new classes to our schedule. Contact us via e-mail or phone and we will meet with you and your child to determine placement options. We can put your child on the waiting list and notify you when a new class is formed.

The minimum class size is three students. Did not find an answer to your Question?

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E-mail us at rsm. Best Louisville Tutoring. Frequently Asked Questions 1. The on-line courses could not provide the critical human element in learning — the ability to interact with students, peers and teachers, to raise questions and share discoveries. RSM's emphasis on algebra nourishes critical and analytic thinking.