Help requested for appropriate books for appropriate courses

[Ancalagon The Black]

Hi everyone,

Warning: A very long post ahead

As this present application season begins, I was doing some checking up on the number and types of courses (in statistics and mathematics) that I have taken. I am currently doing a graduate program in information science at the Indian Statistical Institute (which is regarded as very good school in India)

Sometimes I am a bit confused by the names of courses according to the US system and was wondering if you guys could just tell me if these books and syllabii which I used for my courses here are equivalent to those used in USA.

Moreover, the names of my courses are quite generic and many topics are combined into 1 course, so I was wondering if you guys could tell me the best appropriate US equivalent name for them.

1. Elements of Mathematics I: (4 credits)

Sets, subsets & operations on sets, finite and infinite sets. Relations & properties of relations, equivalence, compatibility, partial order relation, Poset, lub, glb, maximal & minimal elements of a poset. Functions, inverse functions, composition of functions, recursive functions.Logic operators, Truth tables, Normal Forms, Propositional Calculus, Theory of inference and deduction, Predicate Calculus.Boolean functions, min & max terms, simplification of Boolean function with Karnaugh Map & Quine McClusky method, Lattices.Greatest Common Divisors, Euclidean Algorithms, Fibonacci Numbers, Complexity of Euclidean Algorithms, Congruences and Equivalence Relations, Public Key Encryption Schemes, Dividends.Group axioms, permutation groups, subgroups, cosets, normal subgroups, semi-groups, free semi-groups, monoids, sequential machines, error correcting codes, modular arithmetic grammars.Basic Theorems on permutation and combinations. Pigeon hole principle, principle of inclusion and, exclusion. Ordinary & exponential generating functions, recurrence relation, solving recurrence relation by substitution, solving recurrence relation by conversion to linear recurrence relation.Basic definitions trees and graphs, connectivity of a graph, cut poins, cycles, Hamiltonian graphs, Trees, different characterization of trees, bipartite graphs, Planar and Dual graphs. Euler theorem. Algorithms on graphs and trees like Breadth first search & Depth first search, Dijkastra's algorithm for shortest path, Floyd's algorithm for all pair shortest paths, Kruskal's and Prim's algorithm for Minimum cost spanning tree.Languages, Representation of Special languages and Grammars, Finite State Machines, Semigroups, machines and Languages. Machines and Regular Languages, Simplification of Machines

Books Used:
1. Kolman, Busby & Ross "Discrete Mathematical Structures"
2. L.Liu, "Elements of Discrete Mathematics"
3. Peter Linz, "An Introduction to Formal languages and Automata"


2. Elements of Mathematics II:

The existence of Riemann integral for sufficiently well behaved functions. Fundamental theorem of Calculus. Calculus of several variables: Differentiability of maps from Rm to Rn and the derivative as a linear map. Higher derivatives, Chain Rule, Taylor expansions in several variables, Local maxima and minima, Lagrange multiplier.Multiple integrals, Existence of the Riemann integral for sufficiently well-behaved functions on rectangles, i.e. product of intervals. Multiple integrals expressed as iterated simple integrals. Brief treatment of multiple integrals on more general domains. Change of variables and the Jacobian formula, illustrated with plenty of examples. Inverse and implicit functions theorems (without proofs).
Ordinary differential equations - first order equations, Picard's theorem (existence and uniqueness of solution to first order ordinary differential equation), Second order linear equations - second order linear differential equations with constant co-efficients, Systems of first order differential equations, Equations with regular singular points, Introduction to power series and power series solutions, Special ordinary differential equations arising in physics and some special functions (eg. Bessel's functions, Legendre polynomials, Gamma functions). Partial differential equations - elements of partial differential equations and the three equations of physics i.e. Laplace, Wave and the Heat equations, at least in 2D. Lagrange's method of solving first order quasi linear equations.

Books Used:
1. T Apostol: Mathematical Analysis
2. G.F. Simmons: Differential Equations.
3. R. Haberman: Elementary applied partial differential equations.

3. Elements of Statistics:

Sample spaces, Events, Rules of probability, Conditional probability, Independent events, Baye's Theorem, Probability distributions, Continuous random variables, Probability density functions, Expected value of a random variable, Moment, Moment generating functions, Product Moments, Covariance, Multivariate distributions, Marginal distributions, Conditional distributions, Bernoulli distribution, Binomial distribution, Poisson distribution, Geometric distribution, Uniform distribution, Exponential distribution, Gamma distribution, Chi-square distribution, Normal distribution, Bivariate Normal distribution,Distribution of the mean, Distribution of the mean: finite population, Chi-square distribution, t-distribution, F-distribution, Order statistics, Central Limit Theorem, Algorithmic computation of statistical parameters,Unbiased estimators, Method of moments, Method of maximum likelihood.Testing statistical hypothesis, Losses and risks, Tests concerning proportions, Test Concerning, Tests concerning differences between means, Tests concerning variances, Goodness of fit, Linear and Multiple Correlation & regression, Method of least squares etc.

Books Used:

1. Irwin Miller & Marylees Miller, "Mathematical Statistics"
2. Sheldon M Ross, "Probability Models"
3. Sheldon Ross, "A First Course in Probability"

In my undergraduate degree, I have done Calc I, II (Finney), Linear Algebra (Kreyszig), Basic Probability and Statistics upto ANOVA (Levine) as well as some other courses like Linear Programming, Operations Research etc.

Will these combined math/stat courses (I have the highest marks in all of them) meet the minimum requirements for a PhD in IS?

[taxPhD]

Two very very common books used in finance and accounting PhD programs in terms of math/stats are...

Simon and Blume, Mathematics for Economists
- - - this is often used in the summer math bootcamp - - -

Casella and Berger, Statistical Inference
- - - this is often used in a first year stats course - - -

Glancing at the list of topics you listed in your posts, the topics you have covered seem to line up pretty well with what is in these two books.

[oldprogrammer]

1. Elements of Mathematics I: (4 credits)
This is usually a class, for the most part, called Discrete Math. Some computer science programs will call it Discrete Structures. Kenneth Rosen's book seems to be the definitive text for teaching undergraduate discrete math. Other topics might be more like a Discrete Math II or a Graph Theory course, if taught in the Math department, or Automata or Computational Theory if taught in CS.

2. Elements of Mathematics II:
This one's messy. It seems like a few topics from Analysis (at the undergraduate level), and then rest is Ordinary and Partial Differential Equations (which I don't know much about). Hopefully the Analysis topics were handled in a rigorous proof/axiomatic manner and not just as a slightly more advanced Calculus review.

3. Elements of Statistics:
That material and those textbooks are usually covered/used in a 2 semester sequence at the upper division undergraduate or at the intro graduate level, and is probably exactly what the AdComs are looking for.


Are these year-long courses? If not, I would worry that they might be seen as lacking depth (or maybe you ISI guys are really, really smart).

I think you're well prepared mathematically for a PhD in IS. You should only need the math necessary to get through the Economics core, and decent statistics skills for empirical research.

It sounds like you're about 2 years ahead of me in the process. I"m planning on taking Linear Algebra and Intro to Proofs in the Spring, Discrete Math over the summer, and then Analysis in the Fall.

[Ancalagon The Black]

Thanks for the reply guys. I really appreciate it.

oldprogrammer:

All the courses are 4 credits each and are semester courses. We cover a lot of material because we are taught by the professors of the Statistics and Mathematics Unit (who teach in a rather proofy manner). I am worried about the depth factor playing in the minds of the adcoms but believe me, that is exactly what is taught in each course. We get an extremely thorough drilling in each topic and the exams are very hard. I don't exactly know what 4 credits are but we have 4 classes of 2 hours each in each course per week. That is to say, we have 8 hours of classes per course per week and there are 6 such courses plus the thesis (which is year long). :'(

Actually, all this is because the program I am in is a very new program (we are the first batch) and there are students with all sorts of backgrounds (including engineers from IIT who have all learnt this stuff at the undergraduate level) So, to accommodate everyone, they teach all of this in one semester.

You should just see the syllabus of our data structures, algorithms and programming course. It has exactly the syllabus of the 3 corresponding CMU courses in Data Structures, Algorithms and Intro to Java programming. And we learn all of that in 1 semester. I can safely say that none of the topics are missed out by any of the professors and we learn everything at an appreciable depth. I just dont know how to get it across to the adcoms if they have such concerns. I have asked my letter of reference writers to address this in the LORs and I am thinking of preparing a 1 page summary sheet of all relevant courses for each school and put everything in a nice tabular form to show what courses have what.

Any other ideas?

[Ancalagon The Black]

Another question which I wanted to put forward to you oldprogrammer, since you have obviously done so much research into IS PhD programs is that, what courses are required to have a very competitive application into say, a top 10 school.

My major problem is that my GRE scores are not good. (780Q, 710V, 6.0 AWA) [no money/inclination/time to take it again]and without that 800Q, its a dud deal in most good places. Moreover, even though ISI may be very well regarded, my program is a new one and even though my professors regularly publish in places like JASIST or IEEE/ACM Transactions, they are most probably not known to most adcoms.

I am hoping my publications will count. I have 4 international journals (A grade?) and about 12 conference presentations (many different kinds of international conferences since my area is in social networks - no top conference like WWW/GROUP/CSCW etc.)

[oldprogrammer]

Wow, 8 hours per week. I believe it then. Most courses in the US are 3 hours, though courses with discussion or lab sections might be 4 or sometimes 5. I've never heard of a US course of more than 5. So 8 hours *is* practically 3 full classes. I think that is worth a brief note in your statement of purpose. I wouldn't dwell on it, just find a way to be gracious about wanting to make sure that they understand it wasn't just 4 hours a week.

What schools would you consider to be Top 10 IS schools? Personally, I consider CMU, Penn, UT-Austin, and Minnesota to be the best for me, followed by MIT, NYU, Arizona, and Georgia Tech. After that would probably be Michigan, Illinois, Indiana, and Purdue. And for me, "best" means which programs seem to frequently place their graduates well.

Are you kidding me? Your GRE scores are awesome. You're better than 90% on every section. If you don't get into a top school, it won't be because of your GRE.

I think what most programs are looking for is the following:

#1: Can the applicant handle our particularly rigorous course load? In other words, are they mathematically mature enough to to handle an axiomatic approach to both microeconomic theory and probability?
(taking Analysis is a good signal. A course in Microeconomics taught from MWG would also be a strong signal. Having already taken a probability course that required Analysis as a prerequisite would be a strong signal. I think the less pedigree you have (and your letter of reference writers have, the greater the importance in taking advanced math courses.)

#2: Do they know what they are getting into? Do they understand this is 100% about research? How have they demonstrated this?
(Publishing in journals or writing a thesis is probably a good signal of this.)

#3: Do they have what it takes to persevere through it all and complete this program? Can we realistically imagine him becoming one of our peers with our names on his dissertation and the name of our school forever associated on his CV?
(I think a lot of this comes from LORs written by researchers who know you well enough to strongly endorse you in the program you are applying to. Of course, the better the AdCom knows these letter writers, the more weight the letter will have.)


But these are just my musings, so take them with a grain of salt!

[Ancalagon The Black]

Thanks for the kind words oldprogrammer.

Actually, I have already studied upto Intermediate Micro and Macro as well as basic Game Theory from my undergraduate. My grades don't look good (like B or C) but I was amongst the top 3 scorers in class in all of them.

Well, actually, I am looking at several IS programs. For my research activities (social networks analysis and collaborative behavior/CSCW), I found MIT/Stern/Eller to be quite good. I am also applying to Iowa State as a backup. Problem with IS departments are that frequently they are clubbed with operations or other departments like IROMS in Austin. Moreover, most of the schools have small programs.

To make matters more complicated, most of my kind of research is increasingly being done at the large ischools which have good funding so I am applying there. Finally, there are some interdisciplinary programs like in CMU, Northwestern etc. So, its a good mix. I am applying to 15 schools, quite wide ranged in rankings - from Iowa State (strangely, its considered to be top 5 in statistics) to MIT but lets see which way the wind blows in April.

[oldprogrammer]

It doesn't sound like you're really into the economics side of IS, but more into the org (and maybe technical) side. In that case, you probably don't need to think about economics prep too much unless some of these org-based programs still require micro and metrics.

I totally understand where you're coming from. IS is a bizarre field to apply to. Since it has that dichotomy between economics-based and org-based, you first have to filter out those programs that don't really do the research you're interested in. And like you said, most IS departments are a small part of a much larger Operations department. And then when you add in that each program only accepts 0-5 students per year...

I, too, have also found some of the ischools to be interesting, but I was worried too much about placement. It doesn't seem like too many people teaching in ischools have ischool-phds. I've noticed the same in other interdisciplinary fields like bioinformatics, public policy, and education. I'm assuming that, in general, departments don't need to hire a professor with a background in both X and Y since they can hire a professor who specializes in X and another who specializes in Y. PhDs are about depth, after all.

As for me, my interests lie at the intersection of economics and computer science: algorithmic mechanism design, algorithmic game theory, (agent-based) computational economics, etc. So there are about 5 CS programs that fit and a few Econ programs that do. The background I'll have for doing research in this area, coupled with my professional experience, makes me a strong candidate (I hope) for econ-based IS programs from a business intelligence angle. So I'll be applying to probably about 5 or 6 of those. My problem, unfortunately, is going to be LORs. A CS letter is valuable in CS admissions, but less so in IS and Econ. And the same can be said of using an IS or Econ letter for CS admissions - not the most valuable.

[Ancalagon The Black]

Well, I wouldn't quite agree with you about ischools placement. The better ischools are all in the flagship state schools, UCB, UMD, UIUC, UWA, UMich etc.

I have gone through most of the faculty lists in about 15 odd ischools and have found that they frequently hire off each other. This trend has increased dramatically in the last 4-5 years probably because more and more doctoral students are graduating from ischools. The senior faculty are all specialized in each field (like CS or Econ) but the newer assistant professors - those who are doing the most research (since they are all running after tenure) are mostly from other ischools.

What is interesting is that most ischools are guaranteeing funding to those whom they take and are giving very attractive stipends and funding packages. Moreover, I notice that these faculties have a lot of NSF granted projects. I am not really sure of whats going on in the US but I would gather from all this that there is a thrust on information science - maybe from the new Obama administration perhaps? Maybe you know something on this?

It is definitely true that IS research in bschools have waned as of late with only a handful of schools doing any meaningful research. Rather, I am beginning to see a lot of articles from ischool faculty in core MIS journals like MIS Quarterly, Information Systems etc.