Hi, I am Professor James Heffers.
I'm the instructor Math 185 this
semester and I want
to talk to you a little bit about the course.
>> So I want to start off
with hearing what Math 185 is all about.
So I know it's called calculus.
And so how is it different from
the calculus that students have seen in high school?
>> Okay, so 185,
yes, it is called calculus,
but a more accurate thing would be to call it,
it's an introduction to proof writing.
We're using calculus because we know
the students already are familiar with the subject,
but we're not going to be doing like
computations like you would've done
in AP or BC calculus.
We're instead going to be building a foundation
of mathematical rigor and how to write proofs,
and it's a very writing intensive course.
You won't be seeing many numbers of computations,
we'll be doing a lot of proof writing.
Math is mostly, as you go
through it becomes proof writing and rigorous.
And this is like a nice introduction to that world.
>> What is the expected workload of the course?
>> From past experience teaching this,
I know students are usually a little caught off guard.
in the first week, just how long the homework takes.
This isn't going to be like
previous math courses you may have taken,
where you could reasonably
finish the homework in a short time.
These questions require a lot of thinking,
a lot of discussing.
It takes time to write them up.
It definitely would be more than
the workload you would see in
like the standard Calc I-II-III course,
but it would probably be less
than what you would see if you went into the,
the higher 200 Honors Math course. [Math 295]
But it's definitely going to be
several hours a week of homework.
>> What kind of preparation is
expected or helpful for
students to succeed in this course.
>> Obviously doing well
in standard calculus really helps,
like if you got a five on
the BC exam or something like that, that would be great,
but it's also really important,
and again, I can't stress enough that,
that in and of itself isn't enough
to just automatically succeed in this course,
since we're gonna be focused on
building a proof writing skill.
And while familiarity in calculus will help,
It's not going to be that
that in and of itself
isn't gonna be enough for the course.
So while you definitely want that as
a strong background in calculus as preparation.
It also would be good to,
I guess there's really no way to prepare for
this other than just join the class
with the mindset that it's going to be
more than what you were exposed to before.
And understand that the way you learn
things is not necessarily
the end all be all to calculus,
and that there's still much more to explore.
>> What does a typical day in
the class look like,
And how big is the class even?
Tell us what that is like.
>> So I think two years ago,
the class was around like
maybe like 20 students last year in the fall,
at the end of it, it was only maybe like 13,
but I sort of like that because it's
a small enough class size
where we all sort of get to know each other.
We call interact in class.
The class is mostly
lecture driven but with high participation.
Like I might be
doing a proof or something on the board,
but I'm not just gonna sit there talking at the board.
I try to field the audience for ideas.
And we parse through the ideas students have
and we try to figure out which ones we can
run with to actually get this to work and try to
analyze ideas that might seem good.
Maybe find where there's a logical issue
with then. It's usually very interactive.
The students are engaged.
I'm engaged, we all know each other.
Office hours usually end up being,
dare I say, fun.
We all sorta get along and it's been a,
it's been a good experience
because the class sizes are relatively small,
so we all get to know one another.
>> So I get a lot of questions from students.
They come in and say with a five on the BC calc exam,
why would they take Math 185 instead of going
straight into multivariable calculus, Math 215 or Math 285.
>> Well, so I think for some students,
like depending on what they want,
like if they're like physics
or engineering or something like that,
then that perhaps the 215 route is the right route to go.
But 215 doesn't build
your foundation of how to do proof writing.
And again, if you are intending,
on going into mathematics,
this is going to be one of the
most critical skills that you'll
use throughout the entirety of your mathematical career.
And this course sort of serves as a nice gateway into
the world of proof writing because we
we're using a familiar topic.
And we're going to be sort of using that as
the foundation and the, where we start to, let me reword that.
We will use that
familiar topic to our advantage to be able
to discuss it deeper since you
already have some level of comfort with it.
>> What do you personally
like best about teaching this course?
>> Well, that, that, that's a good question.
I sort of, first,
I sort of like getting people to
realize that mathematics is very writing intensive.
That sort of comes as a shock to most people.
They don't think math
and writing usually go hand in hand.
So I sort of do in like enjoy
getting people to sort of realize
that there's a lot of that mathematics.
But I also sort of,
one of the things I really enjoy is getting them to
realize like the things that they've learned so far,
while it seems like you know a lot of mathematics, is
actually quite limited and a small amount of knowledge.
And that math is just this extraordinarily
vast world of theory.
And this is what this course sort of is
a gateway into seeing this.
So I sort of like that aspect of it.
I also like the aspect of getting students to
think beyond routine computations,
to start to think more critically
and problem-solve things in
a way that you can't just use a computer to
figure out, in a way that you need a pen,
paper, your mind and time thinking to figure out.