So you want to study statistics in college. What courses will you need to take? Not only will you be taking classes that pertain directly to statistics, but you will also take classes that are similar, if not identical, to those taken by students majoring in mathematics.
Below is an overview of courses that commonly make up the core of a Bachelor's degree in statistics. Requirements for a degree vary from one institution to another, so be sure to check with your own college or university catalog to be certain what you will need to take in order to graduate with a major in statistics.
Calculus is foundational for many other areas of mathematics. The typical calculus sequence involves at least three courses. There is some variation on how these courses segment the information. Calculus teaches problem-solving and develops numerical competency, both skills that are important for statistics. In addition to this, a knowledge of calculus is necessary to prove results in statistics.
- Calculus One: In the first course of the calculus sequence you will learn to think carefully about functions, exploring topics such as limits and continuity. The main focus of the class will move to the derivative, which calculates the slope of the line tangent to a graph at a given point. Towards the end of the course, you will learn about the integral, which is a way to calculate the area of regions that have strange shapes.
- Calculus Two: In the second course of the calculus sequence you will learn more about the process of integration. The integral of a function is typically harder to compute that its derivative, so you will learn about different strategies and techniques. The other major topic of the course is typically infinite sequences and series. Intuitively, this topic examines infinite lists of numbers, and what happens when we try to add these lists together.
- Calculus Three: The underlying assumption of calculus one and two is that we deal with functions with only one variable. Real life is much more complicated with several variables in the most interesting applications. So we generalize the calculus that we know already, but now with more than one variable. This leads to results that can no longer be depicted on graph paper but need three (or more) dimensions to illustrate.
Other Mathematics Courses
In addition to the calculus sequence, there are other courses in mathematics that are important to statistics. They include the following courses:
- Linear Algebra: Linear algebra deals with the solutions to equations that are linear, meaning that the highest power of the variables is the first power. Although the equation 2x + 3 = 7 is a linear equation, the equations that are of most interest in linear algebra involve several variables. The topic of matrices is developed to solve these equations. Matrices become an important tool to store data in statistics and other disciplines. Linear algebra also directly pertains to the area of regression in statistics.
- Probability: Probability is foundational for much of statistics. It gives us a way to quantify chance events. Starting with set theory to define basic probability, the course will move on to more advanced topics in probability such as conditional probability and Bayes theorem. Examples of other topics may include discrete and continuous random variables, moments, probability distributions, the law of large numbers and the central limit theorem.
- Real Analysis: This course is a careful study of the real number system. In addition to this, the concepts in calculus such as limit and continuity are developed rigorously. Many times theorems in calculus are stated without proof. In analysis, the goal is to prove these theorems using deductive logic. Learning proof strategies is important to develop clear thinking.
Finally, we arrive at what you want to major in, statistics. Although the study of statistics is heavily dependent upon mathematics, there are some courses that do specifically pertain to statistics.
- Introduction to Statistics: The first course in statistics will cover basic descriptive statistics such as average and standard deviation. In addition, some topics of statistical inference such as hypothesis testing will be encountered for the first time. Depending upon the level and aims of the course, there may be a number of other topics. Some courses overlap with probability and will involve a study of different types of probability distributions. Other courses are more data-driven and will focus on how to use computational software to analyze the statistics of these data sets.
- Mathematical Statistics: Here the topics of the introduction to statistics course are dealt with in a mathematically rigorous fashion. There may be few if any data involved in this course. Rather the ideas from most if not all of the mathematics courses are used to deal with statistical ideas in a theoretical way.
- Specialized Courses: There are a variety of other courses that you could then take to earn a degree in statistics. Many colleges and universities have entire courses built around regression, time series, actuarial studies and biostatistics. Most statistics programs require that you complete several of these courses in specialized topics.