Defense

Defense is the easiest skill to learn for a basketball player, in weeks you can become an expert. However, every defense is got to know how geometry is implied so they can know how they can (1) steal more balls, (2) avoid being tricked and (3) stop their mark from scoring. 

1) Stealing: defensive body position enables you to move quickly in any direction. The feet are slightly greater than shoulder-width apart. The body is low to the ground with the knees bent. The back is straight, not bent. Put your weight on the balls of your feet. The fingers are spread apart ready to catch the ball.

2) Confidence: in defensive position, an instant of improper movement like sliding gives the offense an opening. You need to practice staying with the offensive player. Practice maintaining a distance of from two meters to as little as one foot from the mark.

3) Not losing your mark: always force the offense to one side or the other whether or not they have the ball. You need to be aware of which way, right or left, the offense likes or wants to move, and then prevent them from doing so. Forcing involves setting up at about a 45º angle to the mark, one foot to the side. This positioning makes it easier for the mark to go around you one way (the way you want them to) and more difficult to go the other way.

Once again, it is VERY IMPORTANT to be careful with the defensive angles at which you stand your man, when you are half-sided, you have an advantage, as he cannot get pass you as easy as if you faced him directly with no body angle. The same is applied to the angle of you legs on defensive position, the more folded your legs the faster you are. Finally realize that when you displace with the balls of your feet, you also are faster, as there is faster contact with the floor.

Rebounding

60% of rebounding is pure geometry, the rest is wanting to get the ball and timing your jump. In a field shoot, whenever the ball is shot from one side, it will end on the other side most of the time; when shot from the free throw zone it will rebound on the same side. Also, when more force is applied, logically, the rebound will get further. On the other hand, the smaller the force applied, the ball will fall nearer to the place it hit the board or rim. So familiarize yourself with rebounding.
In addition to all this, you should "box-out" (push out your mark so your the closest to the board) to rebound. Anticipation is a great factor in your effectiveness, you not only need to predict where a missed shot will go to be a good rebounder, but also move toward it long before the shot hits the rim.

Dribbling and Passing

A basketball will have a reaction depending on the force you apply to it and the direction you apply it to. Now, predicting this reactions is not rocket science; just Newton´s laws. When you play using a poorly pumped ball, it is very easy to notice it will not bounce as good as when full of air - the same as when you don't angle your moves correctly. 
You have to bounce the ball with a specific amount of force depending on whether you want to project a long pass or a short pass to a teammate, if you are running or walking, and if you are protecting the ball from an opponent or trying to get past them by dribbling.
So you, as a player that understands math, can tell that:
1) When dribbling or protecting the ball, it is better to apply considerable force to it and bounce it quickly and close to the floor for better control.
2) When running you should keep it at the height of your hips or mid-thorax when sprinting so you maintain your speed.
3) A straighter angle is better on long passes (and logically more force) for getting the ball further.
4) A steeper angle will help much more when you are looking for a shorter pass.
5) Remember to aim for the area halfway between you and your teammate to get a better directed pass and that passes are strong and fast, but not so hard that the receiver can't catch it.

Shooting

I thought I could do my first real post about something pretty basic: shooting.

As straightforward as it may seem it is probably the aspect of basketball which involves the most mathematics. To start, you always should build the shot from the ground up:

1)      Firstly you need a strong base for your shot; this should the same for all shots. Feet about shoulder width apart - this will ensure that the base isn’t too narrow or too wide; not causing you neither to have poor balance nor lose explosiveness to score the basket.

2)      Once you have step 1 set, you must ensure that your knees are bent so that you have better balance, power, and more explosiveness in the shot. When you bend your knees, you should also bend slightly at the hips.

3)      This step is where the magic happens. ANGLES. The path the basketball will take once it is shot, comes down to the angle at which it is shot, the force applied and the height of your arms. When shooting from behind the free throw line, a smaller angle of your elbow is necessary (about 45º) to get the ball through the hoop. However, when making a field throw, a larger angle in the elbow is better (the closer to 90º the better). Understanding arcs will help determine how best to shoot the ball. ALSO shooting the ball in an arc will increase its chances of falling through the hoop as you can see in the images. The bigger the arc you choose the better the angle the ball will arrive at to the hoop and it will be more likely that it goes through. The arc you are looking for is one that allows the ball to find the hoop and an angle of about 70º.