Undergraduate: Getting Started

Mathematics is the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter. Since the 17th century, mathematics has been an indispensable adjunct to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.

Math is an abstract language of a universe

Thanks to its abstract nature, math has become the language used in any science. It is used to describe anything that people try to understand in our universe and beyond.

Mathematics is looking for patterns

Mathematicians look for patterns. Such patterns arise from some underlying structure, and one goal of mathematics is to understand this structure. The journey to understand this structure often uncovers new patterns and new structures to study. A striking example of this is the mathematics surrounding the proof of Fermat’s Last Theorem, which says that certain patterns never arise in the integers. In 1637, the amateur mathematician Fermat wrote that he had “a truly marvellous proof of this proposition which this margin is too narrow to contain.” Despite this claim, over 300 years passed before a correct proof was produced.

Its importance is not in the actual statement. Rather, its importance is in the beautiful mathematics that has been generated from it. Some of the most brilliant and influential mathematicians have thought deeply about Fermat’s Last Theorem at one point or another in their careers, including Gauss, Galois, and Euler. Many aspects of modern algebraic number theory have their roots in ideas developed during this time. The modern proof of the result ties together very different parts of mathematics, hinting at a more general underlying structure that will occupy mathematicians for years to come.

Common misconceptions about math and mathematicians

• Mathematics is about correct answers. However, in mathematics the process one arrives to the answer is often much more important than the answer itself.
• Mathematics is a set of rules and formulas that students need to memorize. Students believing in this often feel that their future boss will walk into the office saying “Quick, what’s the quadratic formula?” Or, “Hurry, I need to know the derivative of sin(5x+7).” However, there are no such employers (at least they do not seem to be hiring now).
• In math, students need not to memorize anything. However, one can flip just two letters in a definition or a theorem and you can see your grade falling from A+ to F. Math requires a very high level of exactness and precision (from time to time).
• Mathematicians just crunch numbers in calculators. Some mathematicians surely do a lot of it. However, the key is to know what numbers to crunch. Moreover, the actual crunching is nowadays left to the computers.

Statistics is the scientific discipline that deals with the collection, organization, analysis, display, and interpretation of numerical data. Statistical methods are widely used to design and analyze experiments, surveys, censuses, and other approaches to collecting information about the world. Statistical analyses include the effective summarizing of sets of data and the drawing of inferences from such data, as well as identification of the nature of observational errors and sources of variability that may obscure underlying patterns.

The Nature of Statistics

Statistics provides the reasoning and methods for producing and understanding data. Statisticians are specialists, but statistics demands they be generalists, too.

Mathematics and Computers Are Involved…

Statistics uses mathematics, but it is not abstract or isolated. Statisticians work with people from other professions to solve practical problems. Statistics uses modern computing to organize and analyze data, and statisticians command specialized tools. But the emphasis is on the data to be understood and the problem to be solved, rather than on computing for its own sake.

… But Understanding the Data Is Crucial

Statisticians must know more than statistics. A statistician who works in medicine or in a manufacturing plant or in market research must learn enough medicine or engineering or marketing to understand the data in their setting. Statisticians need the ability to work with other people, to listen, and to communicate.

Statisticians can help to decide whether information is reliable or conclusions drawn from it should be trusted. Statistical methods are used widely in many kinds of work, ranging from research in the biological, social, and physical sciences to applications in law, medicine, government decision-making, finance, accounting, engineering, and actuarial work.