(1.1) What is computer science?

• The study of computers?

  Computer science is no more about computers than astronomy is about telescopes, biology is about microscopes, or chemistry is about beakers and test tubes. Science is not about tools. It is about how we use them, and what we find out when we do. - M. R. Fellows and I. Parberry.

• The study of how to write computer programs?

  Programming is an important part of the field but it's basically just a tool that we use to study new ideas and test new solutions to problems.

  It is not only the construction of a high-quality program that's important but also the methods it uses, the services it provides, and the results it produces.

  It's possible to become so enmeshed in writing code and getting it to run that we forget that a program is only a means to an end, not an end in itself.

• The study of the uses and applications of computers and software?

  Learning to use a word processor, spreadsheet, database system, web browser, etc., is no more a part of computer science than driver's education is a branch of automotive engineering.

  People in all walks of life use software packages. Computer scientists specify, design, build, and test software packages as well as the hardware on which they run.

(1.2) The Definition of Computer Science

According to N. E. Gibbs and A. B. Tucker, computer science is the study of algorithms, including:

1. their formal and mathematical properties (are they correct and efficient;)

2. their hardware realizations (building computer systems that can execute them;)

3. their linguistic realizations (designing programming languages and translating the algorithms into these languages;) and

4. their applications (using them in software packages to solve important problems.)

A dictionary definition of the word algorithm:

n. A procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation; broadly: a step-by-step method for accomplishing some task.

An algorithm is a list that looks something like this:

Step 1	Do something
Step 2	Do something
Step 3	Do something
.
.
.
Step N	Stop, you are finished

There are three different types of operations in an algorithm:

1. A sequential operation carries out a single well-defined task and then the algorithm moves on to the next operation. Examples:
   • Add 1 cup of butter to the mixture in the bowl.
   • Subtract the amount of the check from the current account balance.
   • Set the value of x to 1.

2. A conditional operation asks a question and then selects the next operation to be executed based on the answer to that question. Examples:
   • If the mixture is too dry. then add 1/2 cup of water to the bowl.
   • If the amount of the check is less than or equal to the current account balance, then cash the check; otherwise, tell the person that the account is overdrawn.
   • If x is not equal to 0, then set y to 1/x; otherwise, print an error message that says we cannot divide by 0.

3. An iterative operation tells us to repeat a block of operations. Examples:
   • Repeat the previous two operations until the mixture has thickened.
   • Repeat the following five steps until there are no more checks to be processed.
   • Repeat steps 1, 2, and 3 until the value of y equals +1.

Figure 1.2 in the text shows a formal algorithm for adding two m-digit numbers.

Exercise 7 of Chapter 1 on page 34 of the text shows Euclid's algorithm for finding the greatest common divisor (GCD) of two positive integers I and J.

If we can formally specify an algorithm to solve a problem, then we can automate its solution. That is, we can:

• build a machine (or write a program or hire a person) to carry out the steps in the algorithm;
• the machine (or program or person) doesn't need to understand the concept or ideas behind the algorithm;
• it (or he or she) merely has to do step 1, step 2, step 3, ... exactly as written.

Much of the R&D work in computer science involves discovering correct and efficient algorithms for a wide variety of interesting problems.

Does every problem have an algorithmic solution?

Chapter 11 in the text shows some problems that have no algorithmic solutions. These problems are unsolvable. There's a limit on the ultimate capability of computers.

There are also problems with algorithmic solutions but the algorithms would take so long to execute as to render them useless. For example, one could write an algorithm to always win at the game of chess but it would take more than 10²⁸ years to execute.

There are also problems that humans (even babies) can rapidly solve but do not as yet have efficient algorithmic solutions.

(1.3) Algorithms

The formal definition of an algorithm:

• An algorithm is a well ordered collection of unambiguous and effectively computable operations that, when executed, produces a result and halts in a finite amount of time.

... a well-ordered collection ...

An algorithm is a collection of operations, and there must be a clear and unambiguous ordering to these operations: we must know which operation to do first and after each operation we must know which operation to do next.

As an example the text shows an "algorithm" taken from the back of a shampoo bottle:

Is this a well-ordered set of operations? At step 4 what operations should be repeated?

A well-ordered set of operations can't have ambiguous statements like:

• Go back and do it again. (do what again?)
• Start over. (from where?)
• If you understand this material, you may skip ahead. (skip how far?)
• Do either part 1 or part 2. (how do we decide which part to do?)

... of unambiguous and effectively computable operations ...

The computing agent must be able to understand each and every step of the algorithm. As an example the text shows a possible "algorithm" for making a cherry pie:

Steps 3 and 4 are pretty clear but most of us might need detailed instructions for steps 1 and 2:

The "computing agent" might not understand how to sift the flour in step 1.2 and would need even more detail:

An unambiguous operation is so simple that the computing agent can understand and perform it: we call it a primitive operation or simply a primitive.

Each operation must also be effectively computable. Flapping one's arms until you start to fly or generating a list of all prime numbers are not effectively computable.

... that produces a result ...

We say result instead of answer because sometimes there is no correct answer. The result of an algorithm could be an error message instead of a correct answer.

... and halts in a finite amount of time.

The shampooing "algorithm" has an infinite loop.

(1.4) A Brief History of Computing

(1.4.1) The Early Period: Up to 1940. The first computers used ideas that were developed over hundreds of years by many people:

• 1614: John Napier invented logarithms to simplify mathematical computations.
• 1622: The first slide rule appeared.
• 1672: Blaise Pascal built a mechanical calculator that could do addition and subtraction (Fig. 1.4 in the text.)
• 1674: Gottfried Leibnitz built a mechanical calculator that could also do multiplication and division as well as addition and subtraction.
• 1801: Joseph Jacquard designed an automated loom that could weave complex cloth patterns programmed in a sequence of punched cards (Fig. 1.5 in the text.)
• 1823: Charles Babbage constructed his Difference Engine, a mechanical calculator that was programmed by a sequence of punched cards.
• 1890: Herman Hollerith built punched-card machines that were used to tabulate the 1890 U.S. Census much faster than the previous census.
• 1902: Hollarith left the Census Bureau to found the Computer Tabulating Recording Company to build and sell the punched-card machines.
• 1924: The name of the Computer Tabulating Recording Company was changed to International Business Machines (IBM).

• 1931: The U.S. Navy and IBM jointly funded a project under Prof. Howard Aiken at Harvard University to start building an electromechanical programmable computing device called the Mark I.
• 1939-1942: Prof. John Atanasoff and his graduate student, Clifford Berry, built a computer to solve systems of simultaneous linear equations at Iowa State University.
• 1943: Alan Turing in England directed the building of a computer called Colossus which was used to break the German Enigma code that the Nazis thought was unbreakable.
• 1943: The U.S. Army initiated a project with J. Presper Eckert and John Mauchly of the University of Pennsylvania to build a completely electronic computing device.
• 1944: The Mark I was completed. It could store 72 numbers in its memory and could perform a 23-digit multiplication in 4 seconds.
• 1946: Eckert and Mauchly completed their Electronic Numerical Integrator and Calculator (ENIAC) which was 100 feet long, 10 feet high, and weighed 30 tons (Fig. 1.6 in the text.) The ENIAC was much faster than the Mark I. It could add two 10-digit numbers in 1/5000 of a second and could multiply two numbers in 1/300 of a second.
• 1946: John Von Neumann, a mathematician at Princeton University who worked on the ENIAC project, suggested a fundamentally different computer design called the stored program computer. Instead of programming a computer externally with switches, wires, plugboards and/or decks of punched cards; programs should be encoded with 0 and 1 bits and stored internally in its memory unit along with its data. All computers now use this Von Neumann Architecture.

(1.5) Organization of the Text

The rest of the course and the text is organized into a six-layer hierarchy as depicted in Fig. 1.9 of the text.