README.md 1.68 KB
Newer Older
Jim Hefferon's avatar
Jim Hefferon committed
1 2 3 4 5 6 7
*Introduction to Proofs* is an undergraduate text. 
It is Inquiry-Based, sometimes called the Discovery Method or the Moore Method. 
It is Freely available.

Highlights
==========

Jim Hefferon's avatar
Jim Hefferon committed
8
+ Inquiry-based  
Jim Hefferon's avatar
Jim Hefferon committed
9
    
Jim Hefferon's avatar
Jim Hefferon committed
10 11 12
The text is a sequence of statements for students to prove, along with a few definitions and remarks. 
The instructor does not lecture but instead lightly guides as the class works through the material together. 
For these students, this is the best way to develop mathematical maturity.
Jim Hefferon's avatar
Jim Hefferon committed
13
    
Jim Hefferon's avatar
Jim Hefferon committed
14
+ Covers needed material  
Jim Hefferon's avatar
Jim Hefferon committed
15
    
Jim Hefferon's avatar
Jim Hefferon committed
16 17
We do elementary number theory to the Fundamental Theorem of Arithmetic, sets to DeMorgan's Laws, 
functions to two-sided inverses, and relations up to equivalences and partitions.
Jim Hefferon's avatar
Jim Hefferon committed
18
    
Jim Hefferon's avatar
Jim Hefferon committed
19
+ No prerequisite  
Jim Hefferon's avatar
Jim Hefferon committed
20
    
Jim Hefferon's avatar
Jim Hefferon committed
21 22 23
We enroll sophomore Math majors who typically have taken Calculus III and Linear Algebra. 
But this background isn't a logical prerequisite, it just ensures that students have some mathematical aptitude. 
The material does not presume any college mathematics.
Jim Hefferon's avatar
Jim Hefferon committed
24
    
Jim Hefferon's avatar
Jim Hefferon committed
25
+ Free  
Jim Hefferon's avatar
Jim Hefferon committed
26
    
Jim Hefferon's avatar
Jim Hefferon committed
27 28 29
You can the text without cost. 
You can share it, for instance with students, without cost.
This includes the LaTeX source, so if you are an instructor then you can tune the text to your class.
Jim Hefferon's avatar
Jim Hefferon committed
30

Jim Hefferon's avatar
Jim Hefferon committed
31
+ Flexibility  
Jim Hefferon's avatar
Jim Hefferon committed
32
    
Jim Hefferon's avatar
Jim Hefferon committed
33 34
The text comes in two presentations, one of which is compact enough to just print and hand out on the first day, which is what I do. 
There are a number of other options; see the source.
Jim Hefferon's avatar
Jim Hefferon committed
35
    
Jim Hefferon's avatar
Jim Hefferon committed
36
+ Extras  
Jim Hefferon's avatar
Jim Hefferon committed
37
    
Jim Hefferon's avatar
Jim Hefferon committed
38 39
There is a pack of beamer slides on logic. 
Tese organize the discussions that arise naturally in the first couple of weeks about topics such as the definition of implication.
Jim Hefferon's avatar
Jim Hefferon committed
40
    
Jim Hefferon's avatar
Jim Hefferon committed
41
There is also a pack of slides I show on the first day to introduce students to the class style.