Mathematics Test for MPHIL / PHD

Mathematics Test

 

Overview

• The test consists of roughly sixty six multiple-choice queries / questions drawn from courses remarkably offered at the undergraduate level.
• Approximately fifty  percent of the questions / queries involve calculus and its applications — subject material that's assumed to be common to the backgrounds of almost all mathematics majors.
• About twenty five percent of the questions / queries within the check ar in elementary algebra, linear algebra, abstract algebra, and number theory. The remaining queries upset different areas of arithmetic presently studied by undergraduates in several establishments.

Content Specifications

The following content descriptions may assist students in preparing for the test.The percents given r estimates; actual percents can vary somewhat from one edition of the check to a different.

CALCULUS — 50%

Material learned within the usual sequence of elementary calculus courses — differential and calculus of 1 and of many variables — together with calculus-based applications and connections with analytical geometry,

trigonometry, differential equations; and other branches of mathematics.

ALGEBRA — 25%

• Elementary algebra: basic algebraic techniques and manipulations acquired /  noninheritable in high school and used throughout mathematics
• Linear algebra: algebra, systems of linear equations, vector spaces/ areas, linear transformations, characteristic polynomials, and eigenvalues and eigenvectors
• Abstract algebra (pure mathematics ) and number theory: elementary topics from group theory, theory of rings and modules, field theory, and number theory

ADDITIONAL TOPICS — 25%

• Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability and integrability, and elementary topology of R and Rⁿ
• Discrete mathematics: logic, set theory, combinatorics, graph theory, and algorithms
• Other topics: general topology, geometry, complex/ advance variables, probability and statistics, and numerical analysis

The  mention above descriptions of topics coated within the check mustn't be thought-about exhaustive; it's necessary to know several different connected ideas.. 
Prospective test takers ought to remember that queries requiring no quite a decent precalculus background could also be quite challenging; such queries may be among the foremost troublesome queries on the test.

In general, the queries r meant not solely to check recall of data however conjointly to assess the understanding of elementary ideas and therefore the ability to use those ideas

in various situations

Download the Practice Book