1
00:00:00,000 --> 00:00:02,933
Let's take a look at the table of
contents for the week.

2
00:00:02,933 --> 00:00:05,633
So again,
if you

3
00:00:05,633 --> 00:00:08,633
look at this table of contents
and you see a topic that you like,

4
00:00:08,633 --> 00:00:11,533
just go to that approximate 
minute in the video.

5
00:00:11,533 --> 00:00:15,266
Scale it as appropriate, and 
you can watch that clip.

6
00:00:15,266 --> 00:00:18,500
So we're gonna start off with translation 
from mathematics to English

7
00:00:18,500 --> 00:00:22,000
so how to actually read and write things 
from English to math and math to English.

8
00:00:22,000 --> 00:00:24,966
We talked about contrapositive, 
different types of implications,

9
00:00:24,966 --> 00:00:26,766
contradiction, 
uniqueness,

10
00:00:26,766 --> 00:00:29,366
we also spent a little bit 
time talking about functions,

11
00:00:29,366 --> 00:00:31,333
so injections and 
surjections,

12
00:00:31,333 --> 00:00:33,966
we talked about the 
division algorithm,

13
00:00:33,966 --> 00:00:36,900
and for my class I finished with 
summation/product notation.

14
00:00:36,900 --> 00:00:40,233
I also finished on Friday with 
a bunch of random examples,

15
00:00:40,233 --> 00:00:42,566
which you can check out 
in my lecture 12 notes.

16
00:00:42,566 --> 00:00:46,566
There's just a bunch of problems that you 
have to figure out what technique to use.

17
00:00:46,566 --> 00:00:49,200
It's a very good way to do
mathematics, by the way, to actually

18
00:00:49,200 --> 00:00:52,000
get just a random set of problems and try to do them,

19
00:00:52,000 --> 00:00:54,000
right, because, you know,
on a test and things like that, 

20
00:00:54,000 --> 00:00:56,000
you're gonna be given 
problems in a random order.

21
00:00:56,000 --> 00:00:58,166
They're not gonna be, “Oh 
this is from Chapter 1,

22
00:00:58,166 --> 00:01:00,400
so use Chapter 1 techniques.” 
No, it's gonna be, “Well

23
00:01:00,400 --> 00:01:03,400
this is a topic and you'll have to 
figure out what technique to use.”

24
00:01:03,400 --> 00:01:04,666


25
00:01:04,666 --> 00:01:08,000
So it's a good way to practice and, again, if 
you need to see those or like to see those,

26
00:01:08,000 --> 00:01:11,500
problems and solutions 
are in Chapter 12,

27
00:01:11,500 --> 00:01:13,600
in my Chapter 12 notes, 
at the end of them.