Lec 3 | MIT 18.02 Multivariable Calculus

Lec 2 | MIT 18.02 Multivariable Calculus

Cindy is riding on an elevator in a building that has many
floors and one basement floor underground. Answer these
questions regarding Cindy's adventure riding the elevator up and
down the building.

1) From the first floor, Cindy goes up 8 floors and then down
3 floors. What floor is she now on?
2) Cindy is on the 18th floor. She goes down 10 floors and then
up 13 floors. What floor is she now on?
3) Cindy is on the 7th floor. She then goes up to the 19th floor.
How many floors did she go up?
4) Cindy is on the 2nd floor. She goes down 3 floors. What floor
is she now on?
5) From the top floor, Cindy goes down to the 8th floor,
travelling 17 floors. What is the top floor?
6) Cindy does not know what floor she is on. She presses the
button to go to the 10th floor and the elevator travels 4
floors. What floor was she on originally?

Multivariabel Calculus, Lecture 1, MIT

this is lecture 1 in Multivariable Calculus in MIT

LET ME COUNT THE WAYS

1) Tina has 3 shirts-red, blue, and yellow. She also has 2 skirts-
black and white. Each day, she wears a different shirt with a
different skirt.

A) For how many days can she do this before she must repeat and

Draw pictures of Tina and color if you wish.

There is also a chart called a TREE that can help Tina to know
which outfit is next to wear. It looks like this:

|-----Black
|---Red-------|
| |-----White
|
|
| |-----Black
|--Blue-------|
| |-----White
|
|
| |-----Black
|--Yellow-----|
|-----White

So, you can see all the possibilities and even count them.

C) Uh oh, Tina accidentally ripped her yellow shirt and cannot wear
it anymore. How many outfits does she have now? Draw a tree.

2) When Billy comes home from school each day, he gets a snack
and a drink. His Mom lets him choose either a piece of fruit, a
cookie, or a peanut butter sandwich. He can drink juice,
milk, or a soda.

A) Can you make a TREE that explains all the possibilities of
snacks and sodas? How many snack and drink combinations are there?

B) How many combination are there if the drink is MILK?

The Meaning of Mathematics

When we talk about mathematics, what should we know about it? Is Mathematics about “monster” as many people (who don’t like it) say? Or about mystery for the one who like it?
Many question come from our mind to know and to understand about mathematics. But the answer can be found by reflecting what the really mean of mathematics is. Actually we will not be able to live without mathematics. Everything around us are depend on mathematics.
Mathematics is very useful both in our daily life and in the developing other sciences. Mathematics is science of truth and the body of science. Physics needs mathematics to solve the problem. Chemistry, Biology and other sciences is supported by the useful mathematics.
We can see the mathematics as a science. As a science, Mathematics has objects. The object of mathematics is the material object and formal object. Mathematics material objects are in our minds. We can only imagine the object of mathematics in our minds, because the object of mathematics is abstract, different with the other sciences which is usually the material object is the concrete object as in our daily life.
During this time people think that the material object of mathematics is a numeral. Actually it does not matter if they think like that. However, it needs to straighten the true meaning of mathematics. The numeral is only a symbol to represent a number. Until this time, something what called "seven", we always represents with 7. So in fact we speak about the value of the number of seven, not the numeral of seven. Once again, the symbol is only one way to show us that we think about number seven. We can give another symbol for the number seven.
Actually there are many different symbols to indicate a number. There are Roman numerals, Babylonia numerals, and so forth. Even the numerals have emerged in the very long time. So, essentially if we talk about mathematics, we talk about the values and the characteristics of the objects of mathematics.
The formal object Mathematics is a way of approach to the mathematics material objects. Here, there are many ways of approach in mathematics. As was mentioned above that the Mathematics looks at the characteristics and the value of the object.
Mathematics looks at its object deductively, it means that Mathematics look it in general. For example if we are talking about set, then the attributes attached to the set that must also be attached to the element of the set, otherwise it is not element of the set.
That's a little story about Mathematics, hopefully we can add insight to what is called Mathematics.