Why are Math Class methods called with 'Math.abs()', but Integer Class methods are called with 'static int sum()' or 'int min()'? I think you are confusing some things here. The examples you show for the integer methods are method definitions. That's not calling a method, it's defining one that returns an int. Doesn't the Math Class have max & min methods? So why does the Integer Class also have max and min methods? The Math.max and Math.min methods have overloads for integers, longs, floats, and doubles. But each of those classes have a specific version of the function that just works on its own. It's likely that the Math class is just "proxying" those other methods, based on what you pass into it. It's just there as a convenience, so you don't have to dip down into four different classes for the same functionality. More on reddit.com

The key thing to note is that BigDecimal is decimal. That is, it stores a precise representation of decimal (base-10) numbers. That is, the number is represented as a sum of powers of ten. float and double are binary (IEEE 754). That is, the number is represented as a sum of powers of two. Thus, when you translate a decimal fraction into a binary fraction, you'll end up with errors, because some decimal fractions cannot be represented exactly as binary fractions (within a given precision). These errors add up. The Math functions are intrinsics. They map directly to native routines, which operate on IEEE 754 floating point numbers. Obviously, most floating point units on processors work on IEEE floats (although, I think some older processors could do BCD math). BigDecimal is implemented purely in Java, trading performance for precision, and any math library operating on BigDecimal would have to reimplement all of those math operations in Java, similarly trading performance for precision, to a greater degree. Whether you choose float of BigDecimal depends on your goals. With money, generally the goal is precision, because of the financial consequences of errors in accounting calculations. But, in scientific and engineering application, the goal is reasonable approximation within an error range. I don't think with Black-Sholes you're looking for precision, but approximation. Thus, it is perfectly fine to use float as long as you arrange your calculations to control the error range. Poor arrangement of floating point calculations can significantly widen the error range, resulting wildly deviating results. For this reason, there are books like Numerical Computing with IEEE Floating Point Arithmetic which show you how to arrange floating point calculations to maintain accuracy within a desired error range. EDITED: I don't write good. More on reddit.com

Sounds like an import issue More on reddit.com

Java does not have functions, only methods. Functions are stand alone and exist outside the context of classes. Since this is not possible in Java, it doesn't have functions. Methods exist only in the context of classes. Even methods that one might consider functions abs, sin, etc. only exist in the context of the Math class and therefore are not functions. In Python, you can have both. If you just define a function outside any class, it is a function, yet if you define a function inside a class, it becomes a method. More on reddit.com