Concrete Mathematics : Attack Plan

The first, and most important part of a computer scientist's view of the world is discrete math.

It's like the back-muscle. The cognitive workhorse. The loving parent that keeps the family together. The very heart and soul of the field.

For this portion of keikaku we'll be using the textbook Concrete Mathematics by Graham, Knuth, Patashnik.


Although I haven't used this text before, here's a cursory impression of the material and topics which I'll try to correct as I go through the material.



Chapter 1 : Recurrence Relations
Fairly basic introductory material

Chapter 2 : Sums
List of sums and proving them through recurrences.

Chapter 3 : Integer Functions
Floor, Ceil, their implications

Chapter 4 : Number Theory
Probably the most important chapter in this book

Chapter 5 : Binomial Coefficients
Largest chapter of book

Chapter 6 : Special Numbers
Seems to be more sequences and special tricks

Chapter 7 : Generating Functions
Functions that make sequences

Chapter 8 : Discrete Probability
Combinatorics. This perspective should compound well with my existing knowledge of statistics.

Chapter 9 : Asymptotics
You know. Limits.


I'd like to give each problem a solid attempt and ultimately solve at least half from each chapter. For each chapter, I'll create an ncurses demo for its most interesting concept. If you're following along, I'd recommend listening to some audio lectures found here on this professor's site <--provide link-->. Although all you need is the book, it's good to have audio reinforcement of the concepts.


The problem distribution is as such:

Ch1	Ch2	Ch3	Ch4	Ch5	Ch6	Ch7	Ch8	Ch9
26	37	53	74	114	95	57	63	68

and the difficulty distribution:

Warmup	Basics	Homework	Exam	Bonus	Research
79	122	130	123	109	34

With some basic arithmetic and a simple weight system, we can compute a lower bound to complete all of these.

5*79+10*122+15*130+20*123+30*30 = 6925 minutes = 115 hours, quite a lot, and we should probably expect a larger value in reality.

Distributing the readings and problems over my weekends and after-work schedule, If I'm working at a normal pace, it will take me 3 months to thoroughly cover the entire textbook. Hopefully I might manage in less, though overall I'm happy with this estimate.

Ultimately, without a classroom environment you're the only one that determines your own standard for immersion in the material. A lot can get in the way of that, but let's hope for the best as we chug through the material.