Preparing for the GRE Subject Test in Mathematics: A Comprehensive Guide

Understanding the GRE Mathematics Subject Test

The GRE Mathematics Subject Test consists of approximately 66 multiple-choice questions, covering topics typically found in undergraduate courses. These topics are divided into three main areas:

• Calculus (50%): Differential and integral calculus, sequences, series, differential equations, and limits.
• Algebra (25%): Linear algebra, abstract algebra (groups, rings, fields), and number theory.
• Additional Topics (25%): Real analysis, discrete mathematics, probability and statistics, and complex variables.

Understanding this structure allows you to focus your preparation on the most heavily weighted sections, such as calculus, which makes up half of the exam.

Step 1: Assess Your Current Knowledge

Before starting your preparation, it’s important to assess your current understanding of the topics covered by the test. Begin by reviewing the content outline provided by the ETS and identifying areas where you feel confident or require further study. Taking a practice test early on can help pinpoint your strengths and weaknesses, allowing you to refine your study plan for better efficiency.

Step 2: Gather Study Materials

Effective preparation requires study materials that align with the test’s difficulty and structure. Here are some recommended resources:

• Textbooks: Core undergraduate textbooks such as *Stewart's Calculus*, *Friedberg’s Linear Algebra*, and *Rudin’s Principles of Mathematical Analysis* provide the depth needed for review.
• Practice Problems: Solve a wide range of problems using resources like *Schaum's Outline of Advanced Calculus* and *Schaum's Outline of Linear Algebra*, which offer hundreds of problems with solutions.
• Review Guides: Specialized GRE Math subject test prep books provide practice questions and review key topics. Use these resources to sharpen your problem-solving skills.
• Online Resources: Websites like Khan Academy and MIT OpenCourseWare offer free tutorials covering many of the topics on the GRE Subject Test.

Step 3: Create a Structured Study Plan

Establish a structured study plan based on the test date. Below is a suggested timeline:

• Months 1-2: Topic Review: Focus on calculus and linear algebra. Dedicate time each week to algebra and analysis as well.
• Months 3-4: Focused Problem-Solving: Shift your focus to solving challenging problems, especially in areas identified as weaknesses.
• Month 5: Practice Tests and Final Review: Take full-length practice tests under timed conditions, focusing on areas of difficulty.

This structure will ensure you cover all topics and allow time for review and practice before the test.

Step 4: Practice Under Timed Conditions

Since the GRE Mathematics Subject Test requires solving 66 questions in 2 hours and 50 minutes, time management is crucial. To improve speed and accuracy:

• Time Yourself: Practice solving questions under timed conditions to get used to the pressure.
• Skip and Return: If a problem is too time-consuming, skip it and return later.
• Mental Math: Practice mental calculations, as calculators are not allowed during the test.

Regular timed practice will help you manage the exam more efficiently.

Step 5: Review Key Theorems and Formulas

Memorizing key theorems and formulas is essential. Create a sheet or set of flashcards covering:

• Calculus theorems (e.g., Fundamental Theorem of Calculus)
• Linear algebra identities (e.g., properties of determinants, eigenvalues)
• Abstract algebra concepts (e.g., groups, rings, and fields)
• Real analysis principles (e.g., limits, continuity, differentiability)

Regularly review these as part of your daily study routine to solidify your understanding.

Step 6: Stay Calm and Focused on Test Day

On test day, ensure you're well-rested and confident in your preparation. Keep in mind that the test is designed so that most candidates won’t finish all questions. Focus on solving the problems you know first and make educated guesses for the others if needed.