# Majoring in Math

#### What can I do with a degree in math?

Many students major in mathematics because they want to become math teachers, either at a high school level or at the college or university level. SJSU math alumni also work in industries ranging from aviation safety to risk management to financial planning to satellite design. In fact, one of the three co-founders of Oracle, Edward Oates, graduated from SJSU with a BA Math degree. The MAA website, http://www.maa.org/careers/ is a good place to find out about careers in math.

#### How do I change my major to math?

If you are interested in changing your major to math, please fill out the online 'Contact Us" form and request to see an advisor. After you have talked to an advisor, you need to fill out the change of major form found at the registrar's website and get department approval from Dr. Johnston. The change of major request is subject to department approval and may require approval from AARS.

#### What do I need to change my major to math?

- A C- or better in Calculus I (Math 30 or Math 30P) or AP credit for Calculus I;
- A C- or better in Discrete Math (Math 42);
- A 2.25 GPA or higher in all mathematics courses taken, Precalculus (Math 19) and above.

In addition to the requirements above, all transfer students or students wanting to
change their major to a BA Math or BS Applied Math degree who have 60+ units will
be required to have completed Math 30. 31, 32, and 42 with a grade of C- or better
in each course. Math 32 and 42 could be replaced with any other *approved* upper division course. These students will also be required to have an overall GPA
of at least 2.25 in all math courses taken.

For students transferring to a BA Math or BS Applied Math degree who have 90+ units, in addition to the requirements of the corresponding Change of Major form, students will be required to submit a roadmap to graduation in their proposed major. This may consist of either submitting up-to-date major forms in your current and proposed major, or submitting a semester-by-semester timeline of courses to completion of proposed major. Note that a proposal requiring a significant extension of time to graduation may be denied.

#### What is the hardest part of the major? How do I make it less hard?

That depends on whom you ask. What is difficult to you may not be difficult to others. It is generally agreed that Math 108, Math 128A/B, Math 131 A/B are more abstract, more rigorous and more challenging than some other required courses. You should not plan on taking more than one of those in a regular semester. Each of Math 128 and Math 131 can take up as much time as two regular classes.

**Talking to your advisor **is the best way to work out your difficulties and avoid difficulty situations (such
as taking too many difficult classes). Working with other students and developing
friends and community, such as through the Math Club, is another way to making the process more enjoyable.

#### What does "discrete" and "continuous" math mean?

Roughly speaking, discrete mathematics deals with the mathematics of *countable* things (a countable set is one whose elements can be counted, such as the positive
integers). So number theory, algebra, logic, etc. are closely related to discrete
math. Continuous math is about studying things which cannot be counted this way, like
the real numbers between 0 and 1. Calculus, differential equations, probability, etc.
are more related to continuous math. These mathematics feel different but frequently
help each other.

**What does "pure" and "applied" math mean?**

*Pure* mathematics generally refers to the study of mathematics for its own sake without
any regard to its applications. Even though it is generally associated with rigor
and abstraction, this aspect makes it similar to art. For trained eyes, mathematics
can be beautiful and exquisite, just like a painting. Examples of areas which are
usually considered pure mathematics are abstract algebra, topology, and number theory.
But each of these areas have been applied to real world problems. Lie Algebras are
used in physics, knot theory is being applied to protein folding, and number theory
is used in cryptography. So beautiful mathematics can be useful as well.

*Applied* mathematics is directly motivated by real world problems, but we cannot escape rigor
and abstraction. There are still theorems to be proven, algorithms to be developed
and evaluated, errors to be estimated. Examples of areas commonly considered applied
mathematics are differential equations, numerical analysis, operation research, statistics,
actuarial science. Differential equations is sometimes referred to as the mathematical
language of science and engineering because many laws and principles of science can
be expressed as a differential equation. For example, in calculus you learn that Newton's
second law, F = ma, as applied to a free falling object, can be written as a differential
equation, x"(t)=-g. Applied mathematics is not as simple as "plugging it in". In high
school, you learned how to solve a system of 2 linear equations with 2 unknowns. What
if you have 1,000,000 equations and 1,000,000 unknowns? Can you still use the same
method? Assuming there is a solution to the problem, the answer is "Sure. Why not?".
You can use a method called Gaussian elimination to find the answer to the system
of equations... in theory. We are talking about 1,000,001,000,000 coefficients. That's
a LOT of numbers to remember. And it would require 1,000,000,999,996,500,002 arithmetic
operations (How long are you willing to work on this?) And if you use a computer,
there are other issues like memory, efficiency, accuracy, and stability. The problem
of solving a large or ill-behaved system of equations comes up in so many applications
that we offer an entire course on the subject, Math 143M.