Critique my Coursework (Statistics Related)

College Majors Science Majors
1

<p>Hello!</p>

<p>I am a Statistics/Psychology double major who is interested in pursuing a statistics related field in Graduate school (the Psychology major is there because I originally wanted to go into Psychology but recently changed my mind). I am thinking about biostatistics, mathematical statistics, or psychometrics. Below is a plan I have made for my related (and what I think could be considered related) coursework and their descriptions up until my graduation. The capitalized part is the department of the class. I ask that you critique, rate, or make suggestions for my plan. Are there any semesters that might be overwhelmingly difficult or underwhelmingly easy? Is my coursework sufficient if I want to go to Grad school in one of the fields I am considering? Any recommendations for classes I ought to take in the spots I have open? Are there some classes that are less necessary than others that I ought to drop from my plan to be able to focus more on other classes? Thanks for any guidance you can give me!</p>

<ul>
<li>classes with a star by them are undergraduate/graduate hybrid classes with both undergraduate and graduate students.</li>
</ul>

<p>Fall 2008 (Total Semester Credits: 17)
MATH: Multivariable Calculus (4 credits) - studies functions of several variables including lines and planes in space, differentiation of functions of several variables, maxima and minima, multiple integration, line integrals, and volume.</p>

<p>Spring 2009 (Total Semester Credits 16)
MATH: Elementary Linear Algebra w/ Proofs (3 credits) - includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices.
STAT: Introduction to Statistical Analysis (4 credits) - introduction to the probability and statistical theory underlying the estimation of parameters and testing of statistical hypotheses, including those arising in the context of simple and multiple regression models. Students will use Microsoft Excel to analyze data. Examples and applications are drawn from economics, business, and other fields.</p>

<p>Fall 2009 (Total Semester Credits: 17)
MATH: Introduction to Mathematical Probability (3 credits) - Includes sample spaces, combinatorial analysis, discrete and continuous random variables, classical distributions, expectation, Chebyshev theorem, independence, central limit theorem, conditional probability, and generating functions.
PSYCH: Research Methods and Statistics I (4 credits) - Introduces research methods in psychology, including computer-controlled experimentation, integrated with computer-based exploratory data analysis, and elementary statistical analysis. Three lecture hours, two laboratory hours.</p>

<p>Spring 2010 (Total Semester Credits: 16)
STAT: Introduction to Mathematical Statistics (3 credits) - Includes sampling theory, point estimation, interval estimation, testing hypotheses (including the Neyman-Pearson lemma and likelihood ratio tests), and regression and correlation.
PSYCH: Research Methods and Statistics II (4 credits) - A continuation of discussion of research methods in psychology, including computer-controlled experimentation, integrated with computer-based exploratory data analysis, and elementary statistical analysis. Three lecture hours, two laboratory hours. </p>

<p>Fall 2010 (Total Semester Credits: 16)
STAT: *Applied Linear Models (4 credits) – Linear regression models, inferences in regression analysis, model validation, selection of independent variables, multicollinearity, influential observations, autocorrelation in time series data, polynomial regression, and nonlinear regression.
STAT: Statistical Computing with SAS (3 credits) – The course covers database management, programming, elementary statistical analysis, and report generation in SAS. Topics include: managing SAS Data Sets; DATA-step programming; data summarization and reporting using PROCs PRINT, MEANS, FREQ, UNIVARIATE, CORR, and REG; elementary graphics; introductions to the Output Delivery System, the SAS Macro language, PROC IML, and PROC SQL.
BIOL: Introduction to Biology (3 credits) – Intensive introduction to modern biology designed for natural science majors. Biological structure and function at various levels of organization, cell biology, genetics, development and evolution are covered.
Research Assistant in Psychometric Lab (3 credits)</p>

<p>Spring 2011 (Total Semester Credits: 16)
STAT: *Applied Multivariate Statistics (4 credits) - Topics include matrix algebra, random sampling, multivariate normal distributions, multivariate regression, MANOVA, principal components, factor analysis, discriminant analysis. Statistical software, such as SAS or S-PLUS, will be utilized.
STAT: *Introduction to Mathematical Analysis (3 credits) - Studies statistical distribution theory, moments, transformations of random variables, point estimation, hypothesis testing, and confidence regions.
CS: Introduction to Programming (3 credits) - Introduces the basic principles and concepts of object-oriented programming through a study of algorithms, data structures and software development methods in Java. Emphasizes both synthesis and analysis of computer programs.
BIOL: Introduction to Biology II (3 credits) - Intensive introduction to modern biology designed for natural science majors. Biological structure and function at various levels of organization, cell biology, genetics, development and evolution are covered. This course are required for all biology majors and is a prerequisite for most upper-level biology courses.
Research Assistant in Psychometric Lab (3 credits)</p>

<p>Fall 2011 (Total Semester Credits: ?)
STAT: *Experimental Design (4 credits) – Introduction to the basic concepts in experimental design, analysis of variance, multiple comparison tests, completely randomized design, general linear model approach to ANOVA, randomized block designs, Latin square and related designs, completely randomized factorial design with two or more treatments, hierarchical designs, split-plot and confounded factorial designs, and analysis of covariance.
MATH: Basic Real Analysis (3 credits) – Concentrates on proving the basic theorems of calculus, with due attention to the beginner with little or no experience in the techniques of proof. Includes limits, continuity, differentiability, the Bolzano-Weierstrass theorem, Taylor's theorem, integrability of continuous functions, and uniform convergence.
MATH: Oridinary Differential Equations (3 credits) – Usually offered in the spring, this course covers the same material as MATH 325 with some additional topics, including an introduction to Sturm-Liouville theory, Fourier series and boundary value problems, and their connection with partial differential equations.
[Open Spot]
Research Assistant in Psychometric Lab (3 credits)</p>

<p>Spring 2012 (Total Semester Credits: ?)
STAT: *Categorical Analysis (3 credits) – The course covers topics in categorical data, including contingency tables, generalized linear models, logistic regression, and logit and loglinear models.
MATH: *Introduction to Stochastic Processes (3 credits) – Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory.
[Open Spot]
[Open Spot]
Research Assistant in Psychometric Lab (3 credits)</p>

2

<p>I was not a Stats major, I was a Math major (undergrad) and wondering why would you take Real Analysis instead of just Analysis or Advanced Calculus? </p>

<p>And…why not take Analysis before Real Analysis? If that Real Analysis course uses the Walter Rudin book, just about everybody feels that course is very hard without some “Intro to Analysis” course first.</p>

3

<p>If possible, I’d take the introduction to programming earlier (before Statistical computing using SAS, but if it’s in SAS it’s not really about computational stats…). Real analysis might be worthwhile to take earlier as well, I’m not sure. If your Applied Linear Models does not include Generalized Linear Models (it doesn’t look like it does), you might want to consider that. Finally, anything about Bayesian statistics or numerical analysis would be good to look into as well, assuming such courses are offered.</p>

4

<p>GLOBALTRAVELER:</p>

<p>I was considering including Advanced Calculus. My rationale for not including it was that it seems to not be as big of a priority for Stat-related Grad programs as other classes are. Furthermore, one of professors told me that Advanced Calculus is somewhat similar to Basic Real Analysis. For these reasons and in order to focus more on my other classes, I decided not to include Advanced Calculus.</p>

<p>I am not sure what you mean by Analysis instead of Real Analysis. It also seems that my school does not offer an Analysis course. This is the book that will be used for the Basic Real Analysis at my school next semester: [Amazon.com:</a> Basic Real Analysis (International Series in Mathematics)…](<a href=“http://www.amazon.com/Basic-Real-Analysis-International-Mathematics/dp/0763773182/ref=sr_1_1?s=books&ie=UTF8&qid=1280260845&sr=1-1]Amazon.com:”>http://www.amazon.com/Basic-Real-Analysis-International-Mathematics/dp/0763773182/ref=sr_1_1?s=books&ie=UTF8&qid=1280260845&sr=1-1) </p>

<p>Blobof:</p>

<p>Thanks for your advice! The Categorical Analysis class I plan to take in Spring 2012 seems to cover GLM. </p>

<p>Unfortunately, it is not possible to take the Programming class earlier.</p>

5

<p>Analysis is the same as Real Analysis. Actually Analysis comprises of Real Analysis and Complex Analysis, but you get my point. Either you take Real or Complex.</p>

6

<p>OK, let me chime in some more. I missed the categorical/glm bit, different places have slightly different names and approaches to courses. Advanced calculus is not a bad course to take, but in a way it’s not that useful either, as it will mostly help consolidate multivariate calculus notions. Depending on the school, it might be “equivalent” to analysis but really, to me calculus and analysis are different sides of the same topic. Calculus is the more applied, mechanical type, where the “final result” matters, while analysis is all about proofs and abstract constructs. They both have their uses depending on the situation. Those who only do calculus and never see the abstract side and have a harder time understanding proofs and extensions to the theory, while those who only bother with analysis might not be able to actually integrate their way out of a paper bag (though they’ll prove a solution exist), or, as I’ve seen in statistics, come up with methods that have no value in real life problems.</p>

<p>I was myself a math major back in the day, so I had more core math courses first and fewer statistics and probability courses (over the last two 2 years, 5 courses total). I do see the usefulness of starting with a solid mathematical basis which is why I find it weird to put basic courses like Analysis and ODEs later.</p>

7

<p>Courses labelled “Analysis”, “Real Analysis” and “Advanced Calculus” have no standardized content. Case in point:</p>

<p>At Haverford, Advanced Calculus is a first course in multivariable calculus and Analysis is a first course in real analysis (aka calculus done rigorously). </p>

<p>At Penn, Advanced Calculus is a first course in real analysis, and Real Analysis is an analysis course for PhD students.</p>

<p>At Bryn Mawr, Real Analysis is a first course in real analysis and Analysis refers to the graduate sequence in real and complex analysis.</p>

8

<p>Then how should I interpret it when a Graduate school recommends that applicants take an “Advanced Calculus” course?</p>

<p>Also, no one has mentioned anything about the Bio courses. If I want to do Biostatistics, is it important to take some Bio courses? Is 2 semesters of Intro Bio enough?</p>

9

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<p>Usually a semester or two of undergraduate real analysis, whatever that course is called at your school.</p>

10

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<p>I wouldn’t be so sure. They’d call it analysis in that case, wouldn’t they (or would they)? I would probably recommend both. You need a couple of semester of epsilon/delta proofs (up to measure theory doesn’t hurt, though it can be painful…), but you also need some knowledge of vector calculus. But, when in doubt, contact the department you want to apply to or talk to your profs.</p>

11

<p>I think if it’s just a matter of the “names” of the courses, that can be easily settled by the OP and his/her adviser. Whether it’s called Real Analysis, Analysis, Advanced Calculus, or whatever, doesn’t really matter.</p>

<p>Almost most of the schools I’ve looked at that has the course “Advanced Calculus” [ in the undergraduate level ] is mostly further topics on partial differentiation and vector calculus. “Real Analysis” deals with the theoretical background of calculus in the real number system.</p>

<p>What I think of “Advanced Calculus” is this book and its contents</p>

<p><a href=“Advanced Calculus - David Vernon Widder - Google Books”>Advanced Calculus - David Vernon Widder - Google Books;