About the Department
Mathematics is the language of science, providing a framework for analyzing the world
by abstracting from our observations that which is essential to the question at hand.
A successful study of mathematics gives the student a powerful approach to solving
problems through organization, simplification, and abstraction. This process often
leads to solutions and techniques of great beauty independent of their application.
The aim of the Department of Mathematics is to give its students an understanding
of some of the theories and methods of mathematics as well as an appreciation of their
In today’s job market, individuals with highly developed analytical and problem-solving
skills are in great demand and so there are a number of career options open to the
students who choose to major in Mathematics. These include careers in secondary education,
actuarial science, operations research, scientific computing, management science and
other areas of business. The Department of Mathematics maintains a list of suggested
tracks of courses for different career paths, including a 3:2 Dual-Degree Pre-Engineering
Mathematics majors, including first year students, should seek advisement by a member
of the mathematics faculty as soon as possible.
All students will begin their study of mathematics with Math 176. The Applied Analysis
sequence is an alternative approach to Calculus, which uses a more sophisticated and
rigorous approach and integrates multivariate calculus with single variable calculus.
Placement into Math 176 or Math 278 (Applied Analysis 2 or 3) via AP credit is not
Individuals who do not start their college mathematics with calculus should take Math
105, Math 110, or Math 140, depending on their major interests.
Credit will not be allowed for any course that is taken after the successful completion
of another course for which the first course was a prerequisite.
The mathematics program at Illinois designed to equip our graduates with the skills
needed to succeed in this diverse job market. Click here to learn how.
The book [of nature] is written in mathematical language, and the symbols are triangles,
circles and other geometrical figures, without whose help it is impossible to comprehend
a single word of it; without which one wanders in vain through a dark labyrinth.
Having trouble viewing the booklet? Click here.
|Student Learning Goals of the Mathematics Major
: Analytical Skills
Learning the mathematical language and how to read mathematics.
Understanding the importance of definitions and their use in proofs.
Learning how to formulate mathematical statements (e.g., definition, theorem, axiom,
Learning how to construct and test hypotheses and conjectures.
Developing the ability to create and evaluate mathematical proofs and arguments.
: Rigorous, Logical Thinking Skills
Developing reasoning skills.
Developing habits of clear and precise logical thinking.
◦ Developing habits of clear and precise writing.
◦ Strengthening habits of rigorous logical thought.
Goal 3: Problem-Solving Skills
◦ Developing a knowledge base.
◦ Developing problem identification and problem solving skills.
◦ Learning how to apply and relate mathematics to practical problems.
: Communication Skills
Learning how to read and write mathematical proofs.
Learning how to communicate mathematics in verbal and written form.
: Computer Skills
Learning how to use computers to solve complex problems.
Learning how to use computers to check and apply a theory.