• Lecture 1: Basics (just to get started).
• Homework 1: Triangles (introductory homework).

• Example 1: Quadratic (more complex example, introducing a loop).
• Lecture 2: Selection (much of this was not covered in class).

• Example 2: Craps (a sophisticated and fairly hard example).
• Lecture 3: Repetition (much of this was not covered in class).
• Practice with Loops (practice exercises about loops, with answers)
• Examples 3: Loop Examples (examples to help with Homework 2).
• Example 4: Calculate Pi (example similar to Homework 2).
• Homework 2: Constants (using loops).
• Lecture 4: Loop Patch (a fairly hard example).

• Lecture 5: Functions (an elementary writeup about functions)
• Practice with Functions (practice exercises about functions, with answers)
• Homework 3: Print a Tree (first function homework).

• Lecture 6: Arrays (and Dice) (first array example).
• Lecture 7: Loops and Arrays (reading exam scores and using arrays).
• Lecture 8: Practice with Arrays

                                         //    i    5-i   2*i+1
                                            
            chars(' ',5); chars('*',1);  //    0     5      1
            System.out.println();
            chars(' ',4); chars('*',3);  //    1     4      3
            System.out.println();
            chars(' ',3); chars('*',5);  //    2     3      5
            System.out.println();
            chars(' ',2); chars('*',7);  //    3     2      7
            System.out.println();
            chars(' ',1); chars('*',9);  //    4     1      9
            System.out.println();
            chars(' ',0); chars('*',11); //    5     0      11
            System.out.println();

The program prints:

     *
    ***
   *****
  *******
 *********
***********

I put a little "table" at the right, showing values of i going from 0 to 5, and showing what 5-i and 2*i+1 would then be.

Using this insight, you can write a for loop, letting i take on values from 0 to 5 inclusive. This loop prints the same tree.

   for (int i = 0; i <= 5; i++) {
      chars(' ', 5-i); chars('*', 2*i+1); 
      System.out.println();
   }
 

Now use a variable n in place of 5 (an n that you read in), and the tree is printed at any size. You might ask where the functions 5-i and 2*i+1 come from, but they are also relatively easy. We know there has to be some linear function that gives the right values, so just using a few values, it is easy to construct the correct function.