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(Note: Mods, this is not a maths question per se, so please delete immediately if this is not in line with what is expected here. To all those gearing up to vote down - save it, vote to delete instead.)

I'm planning to buy a few books (Elementary to Intermediate) for the following syllabus. Can you folks recommend a number of books to cover this effectively? I'm not looking for books that will have excessive literature - I'm looking for concice, practice oriented books - something like the Schaum's series.

  • Numbers of books should be low
  • Books should introductory to intermediate, not very advanced
  • Amazon availability would be a huge help

Thanks! The syllabus is below:

TOPICS

1. Solution of Quadratic equations with real coefficients.

2. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

3. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.

4. Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix, inverse of a square matrix, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations using matrices. Gauss-Jordan Method of Solution of simultaneous linear equations.

5. Linear Algebra: Dependence & independence of vectors, bases and dimensions, spanning, properties of quadratic forms.

7. Two dimensions: Cartesian coordinates, distance between two points, shift of origin. Equation of a straight line in various forms, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines; Equation of a circle, equations of tangent, normal and chord.

8. Differential calculus: Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, exponential and logarithmic functions. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, exponential and logarithmic functions. Derivatives of implicit functions; increasing and decreasing functions, maximum and minimum values of a function; partial derivatives; Lagrange’s Mean Value Theorem; Applications: maxima and minima, optimization.

9. Integral calculus: Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties. Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves, continuous compounding, average value of functions.

10. Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

11. Numerical Analysis: solution of polynomial & transcendental equations using numerical methods such as Bisection, Newton-Raphson methods, Lagrange’s and Newton’s Interpolating polynomials.

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Who is this course aimed at and with what goal? It might help to know this to make sensible recommendations? –  Joseph Malkevitch Jun 5 '11 at 17:22
    
This is for an MBA course - more specifically, for a "prelim" test which is conducted at the beginning of the course - it tests whether or not a candidate will be able to handle the mathematical rigor of the course. A decent graduate-level grounding in these topics is expected. (It's a diagnostic exam, not qualifying.) –  BHZ888763 Jun 5 '11 at 21:19
    
if you like the answers, you could upvote them, or even accept one. Or perhaps there is more that you are looking for? –  mixedmath Jun 6 '11 at 13:42
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3 Answers

This is a lot of somewhat varied subjects. Keeping in mind that since I am poor, I implicitly (not anymore) assume that everyone else is poor, here are some books that I recommend.

Quadratic Equations: To be honest here, why don't you just write your own questions? A quadratic equation is of the form $ax^2 + bx + c=0$, so make up your own $a, b, c$ and then solve them. You can check your solution by plugging in your answers and ensuring that you get 0.

Matrices and Linear Algebra: There is a free book and solutions that is available and has many good exercises on linear algebraic things. I would be remiss if I neglected Paul's Online Math Notes on Linear Algebra, because they are excellent notes. The problems come in the form of examples, but if you are disciplined you can attempt to solve them before he does - but you can then immediately check your answer and method. Handy. It seems you also know Schaum's books, so I will assume you have used them already.

Calculus: I again refer you to only widely available things. We have a good book (Dr. Furman's book) with lots of examples and exercises, and some solutions. Again, Paul's Online Notes on Calculus are exceptional. If you are insistent on buying something (actually spending money... ugg) then I would recommend either Calculus in One and Several Variables by Salas, Hille, and Etgen; or I would recommend an AP Calculus review (I am fond of Barron's over Princeton Review). But the former is a fully functional book for intro college courses and the latter doesn't teach much of anything - and I don't really know what you're looking for or rather why you are motivated to get these problem books.

For your other topics, I don't have a clear idea of how much depth or what style of questions you want. For example, Paul has notes on pre-algebra as well, which certainly covers what you call 'two dimensions' - but these skills are largely mastered before you start learning calculus. An AP practice book (again, Barron's over Princeton Review) on Probability and Statistics will have lots of questions on combinations and permutations, for example. But many are freely available online. And your AHG sequences and sums - what do you want? Do you literally just want sequences, to find means and sums? If so, make your own. If you doubt an answer, post it here and we can guide you. But maybe you're looking for something more?

It's hard to say, but that's what I would recommend.

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Thanks a bunch for the links, always better than having to buy books. Paul's notes (which I didn't know about) are excellent, I must say. –  BHZ888763 Jun 5 '11 at 21:19
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I think you might want to take a look at Apostols' Calculus volumes I and II here and here. They easily cover your caclulus, linear algebra and differential equations topics (and more) and are very well-written. Unfortunately however they are obscenely expensive so it would probably be a good idea to review them at the libary and make sure they serve your needs before you actually purchase them.

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Stewart Calculus: Early Transcendentals and Lay's Linear Algebra and It's Applications Will cover 2,4,5,8,9 and get you started on 10 If you're concerned with price just buy an older edition there are plenty on Amazon.

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