# AnalyticBridge

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# \$33,000 to get an outdated Applied Maths degree, offering no job prospects

From University of Washington, Seattle. Curriculum puts emphasis on numerical analysis, digital filtering, image de-blurring, contour detection and techniques that are 30 to 40 years old. I tried to get an exact price quote, but couldn't find again the web page where the price is listed.

Clearly a service that is priced based on costs (paying salaries to Professors that have been doing the exact same research and teaching for 30 years), rather than on value. And hiding the price (there's an application form, but it does not tell you how much it will cost you). You can learn all this stuff in books published 25 years ago, maybe in just one single book called Numerical Recipes and sold for \$150, and frankly, it's not a good usage of your time learning this stuff, whether you pay for it or not.

AMATH 301 Beginning Scientific Computing (4) NW
Introduction to the use of computers to solve problems arising in the physical, biological and engineering sciences. Application of mathematical judgment, programming architecture, and flow control in solving scientific problems. Introduction to MATLAB routines for numerical programming, computation, and visualization. Prerequisite: either MATH 125, Q SCI 292, MATH 128, or MATH 135. Offered: AWSpS.
Instructor Course Description: Eli Shlizerman

AMATH 351 Introduction to Differential Equations and Applications (3) NW
Introductory survey of ordinary differential equations. Linear and nonlinear equations. Taylor series. Laplace transforms. Emphasis on formulation, solution, and interpretation of results. Examples from physical and biological sciences and engineering. Introduction to MATLAB as a tool for solving differential equations. Prerequisite: MATH 125. Offered: AWSpS.
Instructor Course Description: Yun Zhang

AMATH 352 Applied Linear Algebra and Numerical Analysis (3) NW
Analysis and application of numerical methods and algorithms to problems in the applied sciences and engineering. Applied linear algebra, including eigenvalue problems. Emphasis on use of conceptual methods in engineering, mathematics, and science. Extensive use of MATLAB package for programming and solution techniques. Prerequisite: either MATH 126 or Q SCI 293. Offered: AWSpS.

AMATH 353 Fourier Analysis and Partial Differential Equations (3) NW
Heat equation, wave equation, and Laplace' s equation. Separation of variables. Fourier series in context of solving heat equation. Fourier sine and cosine series; complete Fourier series. Fourier and Laplace transforms. Solution of partial differential equations on infinite domains. D' Alembert' s solution for wave equation. Prerequisite: either AMATH 351 or MATH 307. Offered: Sp.

AMATH 383 Introduction to Continuous Mathematical Modeling (3) NW
Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results. Prerequisite: either AMATH 351 or MATH 307. Offered: AWS.

AMATH 401 Vector Calculus and Complex Variables (4)
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. Prerequisite: MATH 126. Offered: A.

AMATH 402 Introduction to Dynamical Systems and Chaos (4)
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology. Prerequisite: either AMATH 351 or MATH 307. Offered: W.

AMATH 403 Methods for Partial Differential Equations (4)
Applications of partial differential equations; linear and quasilinear first order equations, characteristics, shocks; classification of linear second order equations; basic solution techniques for parabolic, elliptic, and hyperbolic equations; Green' s functions and integral transform methods. Prerequisite: AMATH 402. Offered: Sp.

AMATH 422 Computational Modeling of Biological Systems (3)
Examines fundamental models that arise in biology and their analysis through modern scientific computing. Covers discrete and continuous-time dynamics, in deterministic and stochastic settings, with application from molecular biology to neuroscience to population dynamics; statistical analysis of experimental data; and MATLAB programming from scratch. Prerequisite: either MATH 307 or AMATH 351. Offered: A.

AMATH 423 Mathematical Analysis in Biology and Medicine (3)
Focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications drawn from many branches of biology and medicine. Provides experiences in applying differential equations, difference equations, and dynamical systems theory to biological problems. Prerequisite: either AMATH 351 or MATH 307, MATH/STAT 390. Offered: Sp.

AMATH 424 Mathematical Biology: Spatiotemporal Models (3)
Examines partial differential equations for biological dynamics in space and time. Draws examples form molecular and cell biology, ecology, epidemiology, and neurobiology. Topics include reaction-diffusion equations for biochemical reactions, calcium wave propagation in excitable medium, and models for invading biological populations. Prerequisite: AMATH 353. Offered: Sp.

AMATH 481 Scientific Computing (5)
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social, and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results. Prerequisite: AMATH 301. Offered: A.

AMATH 482 Computational Methods for Data Analysis (5)
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of stastistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression. Offered: W.

AMATH 483 High-Performance Scientific Computing (5)
Introduction to hardware, software, and programming for large-scale scientific computing. Overview of multicore, cluster, and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development. Prerequisite: either CSE 142 or AMATH 301. Offered: Sp.

AMATH 490 Special Topics (1-5, max. 15)
Topics of current interest in applied mathematics not covered by other undergraduate courses.

AMATH 498 Senior Project or Thesis (1-6, max. 6)
Intended for Honors students and other advanced undergraduates completing a special project or senior thesis in applied mathematics. Offered: AWSpS.

Credit/no credit only. Offered: AWSpS.

AMATH 500 Special Studies in Applied Mathematics (*, max. 24)
Lectures and discussions of topics of current interest in applied mathematics. May not be offered every quarter; content may vary from one offering to another. Prerequisite: permission of instructor.

AMATH 501 Vector Calculus and Complex Variables (5)
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration.

AMATH 502 Introduction to Dynamical Systems and Chaos (5)
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology.

AMATH 503 Methods for Partial Differential Equations (5)
Applications of partial differential equations; linear and quasilinear first order equations, characteristics, shocks; classification of linear second order equations; basic solution techniques for parabolic, elliptic, and hyperbolic equations; Green' s functions and integral transform methods.

AMATH 504 Mathematical Epidemiology (5)
Focuses on the construction and analysis of mathematical models for infectious disease transmission and control. Emphasizes evaluation and comparison of vaccination programs. Applications are presented for a variety of diseases such as measles, rubella, smallpox, rabies, etc. Prerequisite: AMATH 351 or equivalent. Offered: Sp; odd years.

AMATH 505 Introduction to Fluid Dynamics (4)
Eulerian equations for mass-motion; Navier-Stokes equation for viscous fluids, Cartesion tensors, stress-strain relations; Kelvin' s theorem, vortex dynamics; potential flows, flows with high-low Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory. Prerequisite: AMATH 403 or permission of instructor. Offered: jointly with ATM S 505/OCEAN 511; A; odd years.

AMATH 506 Applied Probability Statistics (4)
Discreet and continuous random variables, independence and conditional probability, central limit theorem, elementary statistical estimation and inference, linear regression. Emphasis on physical applications. Prerequisite: some advanced calculus and linear algebra. Offered: jointly with STAT 506.

AMATH 507 Calculus of Variations (5)
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods. Prerequisite: AMATH 351 or MATH 307; MATH 324, 327; recommended: AMATH 402 and AMATH 403 or MATH 428 and 429. Offered: W; odd years.

AMATH 512 Methods of Engineering Analysis (3)
Applications of mathematics to problems in chemical engineering; vector calculus; properties and methods of solution of first and second order partial differential equations; similarity transforms, separation of variables, Laplace and Fourier transforms. Offered: jointly with CHEM E 512; A.

AMATH 514 Networks and Combinatorial Optimization (3)
Networks and directed graphs. Paths and trees. Feasible and optimal flows and potentials. Transportation problems, matching and assignment problems. Algorithms and applications. Prerequisite: MATH 308 or AMATH 352 and MATH 324. Offered: jointly with MATH 514.

AMATH 515 Fundamentals of Optimization (5)
Maximization and minimization of functions of finitely many variables subject to constraints. Basic problem types and examples of applications; linear, convex, smooth, and nonsmooth programming. Optimality conditions. Saddlepoints and dual problems. Penalties, decomposition. Overview of computational approaches. Prerequisite: linear algebra and advanced calculus. Offered: jointly with IND E 515/MATH 515.

AMATH 516 Numerical Optimization (3)
Methods of solving optimization problems in finitely many variables, with or without constraints. Steepest descent, quasi-Newton methods. Quadratic programming and complementarity. Exact penalty methods, multiplier methods. Sequential quadratic programming. Cutting planes and nonsmooth optimization. Prerequisite: AMATH 515. Offered: jointly with MATH 516.

AMATH 521 Special Topics in Mathematical Biology (5, max. 15)
DNA-folding, patter-forming systems, stochastic analysis. Prerequisite: AMATH 402 or equivalent. Offered: Sp.

AMATH 522 Introduction to Mathematical Biology (5)
Modeling biological systems with differential and difference equations. Examples from: ecology (population growth, disease dynamics): biochemistry and cell biology; and neurobiology (Hodgkin-Huxley and neural networks). Methods include linear stability analyses, phase-plane analyses, and perturbation theory.

AMATH 523 Mathematical Analysis in Biology and Medicine (3)
Focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications drawn from many branches of biology and medicine. Provides experiences in applying differential equations, difference equations, and dynamical systems theory to biological problems. Offered: W.

AMATH 524 Mathematical Biology: Spatiotemporal Models (5)
Examines partial differential equations for biological dynamics in space and time. Draws examples form molecular and cell biology, ecology, epidemiology, and neurobiology. Topics include reaction-diffusion equations for biochemical reactions, calcium wave propagation in excitable medium, and models for invading biological populations. Offered: Sp.

AMATH 531 Mathematical Theory of Cellular Dynamics (3)
Develops a coherent mathematical theory for processes inside living cells. Focuses on analyzing dynamics leading to functions of cellular components (gene regulation, signaling biochemistry, metabolic networks, cytoskeletal biomechanics, and epigenetic inheritance) using deterministic and stochastic models. Prerequisite: AMATH 402' AMATH 403; course in probability.

AMATH 533 Neural Control of Movement: A Computational Perspective (3) Todorov
Systematic overview of sensorimotor function on multiple levels of analysis, with emphasis on the phenomenology amenable to computational modeling. Topics include musculoskeletal mechanics, neural networks, optimal control and Bayesian inference, learning and adaptation, internal models, and neural coding and decoding. Prerequisite: vector calculus, linear algebra, MATLAB, or permission of instructor. Offered: jointly with CSE 529; W.

AMATH 535 Mathematical Ecology (5) Kot
Considers models, methods, and issues in population ecology. Topics include the effects of density dependence, delays, demographic stochasticity, and age structure on population growth; population interactions (predation, competition, and mutualism); and application of optimal control theory to the management of renewable resources. Offered: Sp.

AMATH 540 Introduction to Computational Finance and Financial Econometrics (5) Zivot
Covers probability models, data analysis, quantitative, and statistical methods using applications in finance, and introduction to and use of the R programming system for data analysis and statistical modeling. Prerequisite: calculus through multivariate calculus; introductory probability and statistics. Offered: AS.

AMATH 551 Introduction to Trading Systems (3)
Introduces electronic trading systems. Uses the R programming language to develop, evaluate, and optimize quantitative trading strategies. Students apply trading strategies through a live paper-trading account with an online broker using real time market data.

AMATH 567 Applied Analysis (5)
Reviews applications of metric and normed spaces, types of convergence, upper and lower bounds, and completion of a metric space; Banach spaces and Hilbert spaces, bounded linear operators, orthogonal sets and Fourier series, and the Riesz representation theorem; and the spectrum of a bounded linear operator and the Fredholm alternative. Introduces distributions. Recommended: AMATH 401 or equivalent. Offered: A.

AMATH 568 Advanced Methods for Ordinary Differential Equations (5)
Survey of practical solution techniques for ordinary differential equations. Linear systems of equations including nondiagonable case. Nonlinear systems; stability phase plane analysis. Asymptotic expansions. Regular and singular perturbations. Recommended: 402 or equivalent. Offered: W.

AMATH 569 Advanced Methods for Partial Differential Equations (5)
Analytical solution techniques for linear partial differential equations. Discussion of how these arise in science and engineering. Transform and Green' s function methods. Classification of second-order equations, characteristics. Conservation laws, shocks. Prerequisite: AMATH 403, AMATH 568 or MATH 428 or permission of instructor. Offered: Sp.

AMATH 570 Asymptotic and Perturbation Methods (5)
Asymptotics for integrals, perturbation and multiple-scale analysis. Singular perturbations: matched asymptotic expansions, boundary layers, shock layers, uniformly valid solutions. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or permission of instructor. Offered: A.

AMATH 572 Introduction to Applied Stochastic Analysis (5)
Introduction to the theory of probability and stochasitc processes based on differential equations with applications to science and engineering. Poisson processes and continuous-time Markov processes, Brownian motions and diffusion. Prerequisite: AMATH/STAT 506, AMATH 402, or equivalent knowledge of probability and ordinary differential equations. Offered: Sp; even years.

AMATH 573 Coherent Structures, Pattern Formation and Solitons (5)
Methods for nonlinear partial differential equations (PDEs) leading to coherent structures and patterns. Includes symmetries, conservations laws, stability Hamiltonian and variation methods of PDEs; interactions of structures such as waves or solitons; Lax pairs and inverse scattering; and Painleve analysis. Prerequisite: AMATH 569, or permission of instructor. Offered: A; odd years.

AMATH 574 Conservation Laws and Finite Volume Methods (5)
Theory of linear and nonlinear hyperbolic conservation laws modeling wave propagation in gases, fluids, and solids. Shock and rarefaction waves. Finite volume methods for numerical approximation of solutions; Godunov' s method and high-resolution TVD methods. Stability, convergence, and entropy conditions. Prerequisite: AMATH 586 or permission of instructor. Offered: W.

AMATH 575 Dynamical Systems (5)
Overview of ways in which complex dynamics arise in nonlinear dynamical systems. Topics include bifurcation theory, universality, Poincare maps, routes to chaos, horseshoe maps, Hamiltonian chaos, fractal dimensions, Liapunov exponents, and the analysis of time series. Examples from biology, mechanics, and other fields. Prerequisite: AMATH 568 or equivalent. Offerd: Sp; odd years.

AMATH 579 Intellegent Control through Learning and Optimization (3)
Design or near-optimal controllers for complex dynamical systems, using analytical techniques, machine learning, and optimization. Topics from deterministic and stochastic optimal control, reinforcement learning and dynamic programming, numerical optimization in the context of control, and robotics. Prerequisite: vector calculus; linear algebra, and Matlab. Recommended: differential equations; stochastic processes, and optimization. Offered: jointly with CSE 579.

AMATH 581 Scientific Computing (5)
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social, and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results.

AMATH 582 Computational Methods for Data Analysis (5)
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression. Offered: W.

AMATH 583 High-Performance Scientific Computing (5)
Introduction to hardware, software, and programming for large-scale scientific computing. Overview of multicore, cluster, and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development. Offered: Sp.

AMATH 584 Applied Linear Algebra and Introductory Numerical Analysis (5)
Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations. Offered: jointly with MATH 584; A.

AMATH 585 Numerical Analysis of Boundary Value Problems (5)
Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse symmetric and non-symmetric linear systems: conjugate-gradients, preconditioners. Prerequisite: AMATH 581 or MATH 584 which may be taken concurrently. Offered: jointly with MATH 585; W.

AMATH 586 Numerical Analysis of Time Dependent Problems (5)
Numerical methods for time-dependent differential equations, including explicit and implicit methods for hyperbolic and parabolic equations. Stability, accuracy, and convergence theory. Spectral and pseudospectral methods. Prerequisite: AMATH 581 or AMATH 584. Offered: jointly with ATM S 581/MATH 586; Sp.

AMATH 600 Independent Research or Study (*)
Credit/no credit only.

AMATH 700 Master' s Thesis (*)
Credit/no credit only.

AMATH 800 Doctoral Dissertation (*)
Credit/no credit only.

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Comment by lisa jenkins on December 19, 2012 at 2:37pm

for me "going to school" is more about making me actually do the work and getting some kind of feedback that I am understanding the concept.  Yes, you can just as easily read a book, but there is something about being held accountable for it (by having to pay \$\$ to take the class, attend the class), which ensures I put in the time to actually learn the concepts.  Working full-time and having a busy home life makes it far to easy to never start or start and not finish.  But the only way to know for sure that you have a grasp of the concepts is to work on a project.  Projects give you the confidence to KNOW you understand the concepts well enough to know when and how to apply them.

I too shelled out quite a pretty penny to get a MS in Operations Research degree, only to almost complete it before the program stopped offering classes.  I want to do analytics, so now I find myself having to transfer to another program, probably an analytics based one (aka Northwestern U.).  Did I waste money??  Probably.  Are the skills I learned transferable?  ABSOLUTELY.  With the right foundation, you can grasps changes in methodology, subject matter, whatever. That's how I look at it.

Comment by Mikhail Kozine on June 11, 2012 at 12:50pm

First of all, you can not learn from a book, and especially from "Numerical recipes". It is a brilliant book, but if you really want to learn - that is to comprehend a subject, not only be aware of its existence - you better read another couple of books on a particular method, do a real project, or better yet -  go to a college.

Second - it all is very opinionated. The courses listed in this message are mostly oriented to application to physics and biology. You would prefer a courses for business analytics? Fine. Let's take a closer look at Jean-Pauls dream set. How these can be modern subjects, if they all are at least half-a-century old:

• design of experiments, cross-validation
• fraud detection, rule systems, associations detection, scoring systems
• imputation methods
• six sigma
• root cause detection

Bottom-line: Don't blame the professors. They teach as they can. You still can a lot from them. The rest is in your hands. And be aware of what modern business really needs - this is where professors can be of more help, I admit.

Comment by Vincent Granville on July 9, 2011 at 11:36am

Many people suggest that these classes are still very useful, and the purpose of University is to learn how to learn, not to get the newest skills, which could be outdated very quickly anyway.

There's some truth to this, but then my question is: why spend \$33,000 on these classes when you can learn the same material from books, much faster than by attending classes, and for a tiny fraction of the cost?

Comment by Oleg Okun on July 9, 2011 at 12:19am

There is a gap between science and industry. Though science is the only locomotive of technological progress, many managers in industry didn't and still don't understand its importance. It is because in the past the MBA degree was all one needed to have in order to become a manager. As a result, such managers look and act as overseers equipped with whips rather than with knowledge. However, modern and future business problems are much more complex than those encountered twenty years ago, so that each manager must be technically competent in order to successfully handle them. We live in times of disappearance of general managers and appearance of a new group - technically and business-competent managers. This transition might look slow but it is happening.

Comment by Amanpreet Singh on July 8, 2011 at 11:34pm
Well i agree that rarely a university recruits professional data scientist from the real world who can go beyond the books and text. Im not saying that academic knowledge is not useful, in-fact i personally favor the academic side of data analysis but the fact that recent graduates still have to rely on private certifications to get a decent job can be a little frustrating.
Comment by Oleg Okun on July 8, 2011 at 5:12am

Tenure is to blame for mediocre teaching as a tenured position protects its holder from all troubles/worries of someone with a temporal contract. As a result, professors often are not interested to update a teaching curriculum according to requirements of real life. In order to correct the situation, all tenured positions for senior staff members in Universities must be abolished and replaced with 3-5 year contracts. If during this period, the current holder of a professorial position didn't demonstrate results superior to those of his/her competitors, then a new contract will be given to another, more skillful and hard-working applicant. Such rules would force professors not only to constantly follow labor market needs, but also to forge links with industry.

Universities need to be run as companies, with professors acting like scientific managers who are responsible for certain KPIs.

Comment by Michael Tuchman on June 30, 2011 at 12:02pm

It's easy to say, "I'll take these modern courses instead of old fashioned ones".  And indeed, with a good college education you can, and should, further your education with more  up to date courses.  But how do you structure a degree whose value will last 50 years, even as the the trendy analytical techniques come and go.

The problem with customers is that they keep confusing college with trade school.  If you can teach yourself what you need to know, that's great, but how is it you can do that? Perhaps because of your college background that taught you how to think critically?

I agree with Gregory.

Comment by Vincent Granville on June 20, 2011 at 8:18pm

Probably the biggest issue is how university professors are recruited and tenured, and (as a consequence) the fact that most universities are very slow to integrate new strategic courses in their curriculum. For instance, most of what I do today is not taught in any university programs.

Yet no university has ever successfully invited an expert data scientist (from the business world) to teach a course that could really help students get new jobs, such as "design of analytic APIs for big data, with practical application to search and taxonomy technology". Indeed, nobody teaches stuff like that, as far as I know. Yet start-ups and corporations contact the best business scientists every day to check whether they might be interested in joining their staff to work on such projects.

Comment by Gregory Piatetsky-Shapiro on June 20, 2011 at 7:41am
The curriculum is outdated, but I disagree that the degree is useless.  Applied math degree shows that a person can learn hard math stuff and has analytic skills.  Today's technology is evolving so rapidly, that what is being used today was probably not taught 5 years ago anywhere, so an advanced degree is as much training in how to learn as it is specific knowledge.  My PhD was on Databases/AI and perhaps only 10% of what I learned in school I actually used in any of my jobs or consulting.
Comment by Welma Pereira on June 20, 2011 at 2:33am
I do not think this course is worth \$33,000 but I think the content of the course is better than a numerical analysis book.

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