Dear Sandeep:
Your appreciation for mathematics makes you a suitable candidate for pursuing a technical education. As you continue your studies, your area of focus would inevitably become narrow but deep. In other words, you will learn a lot more about fewer things. So far in school, you have studied many subjects, arguably with nearly equal focus and depth. Now comes the time when you have to decide which area of education you wish to pursue. Your choice should be a balance between what you like to do and what financial rewards you can get. Money alone may not be the right criterion for your selection.
A text book definition of engineering is application of science to the design, building, and use of machines. For example, electrical engineering deals with electrical machines, and computer engineering deals with computing machines. In the beginning of engineering programs, there is considerable overlap between various branches of engineering. Then you begin to focus in more and deeper into a particular area. Regardless of the branch of engineering, your interest in mathematics will stand you in good stead.
The programs for the study of computers basically come in two flavors: computer engineering and computer science. The two fields have considerable overlap but the basic difference is that computer engineering has a greater focus on the computer hardware and computer science has a greater focus on computer software. Either way, you would work a lot with computers.
Computer hardware is the physical computers and computing machines. Thus, computer engineering deals with the fundamentals of computer design. You would study the design, construction, and testing of both basic and sophisticated computing machines. You would also learn computer communications and networking, including the Internet. All in all, you would spend considerable time in laboratories to first learn how computer subsystems work and then test your own designs of computers and computer networks. You would also learn computer software, but not to the extent you would learn if you were pursuing computer science. This is where the overlap with computer science comes in.
Computer software refers to the programs that make the computer hardware function. Windows 98 is an example of a program, called the operating system, which makes your PC behave in a particular way. Microsoft Word, Netscape Navigator, and ICQ are examples of programs, which are also called applications. Applications exploit the behavior of the computer, after the operating system has been installed, to perform certain functions in a particular and desired fashion. Computer programs are written in many languages, such as C++, Visual Basic, Java, etc. A computer science program will teach you algorithms and techniques for creating these applications. You will spend a lot of time on the computer to write and test your programs. You will also learn some of the basics of computer hardware, which is thus an overlap with computer engineering. But your main interaction with computers will be more as a user and code developer than as a builder; that is, you will be trained to be a programmer, not a manufacturer.
To give a point of comparison, let us talk about electrical engineering, which perhaps is the engineering discipline that has the greatest overlap with computer engineering and computer science. Electrical engineering deals with the design of electrical machines, analysis of electrical signals, physics of electronic devices, etc. Since computers are one form of electrical machines, you would learn about computer hardware and software. However, there is more to machines, signals, and physics than just computers. So you would learn about many more electrical machines in electrical engineering than you would in computer engineering or computer science. Here again, you would spend time in the laboratory to test your own designs, including those of computers. Many electrical engineering programs also allow for a specialization in computer engineering. Your classes in electrical engineering will include a great deal of mathematics. The use of computers would definitely be a utility to do your homework assignments.
Now comes the tricky question of which career, engineering or computers, pays more. We can talk about this with some certainty in today's job market. Computer science and computer engineering graduates command some premium, not great premium, over electrical engineering graduates upon graduation. However, with some job experience, computer science and computer engineering graduates have seen considerably greater financial compensation than their electrical engineering counterparts. It is harder to predict whether that would be true in 5 or 10 years from now. However, we can venture to reach some reasoned conclusions. With the advent of the Internet and onslaught of the information economy, the demand for "computer savvy" individuals will continue to grow in the foreseeable future. Eventually, the supply and demand of computer engineering and computer science graduates will determine their value in the marketplace, as it does for all other fields.
Sandeep, we hope this information is helpful. We wish you a highly successful future!