541 Why This Is Important Mathematical systems can be used to solve a variety of problems that involve timekeeping, work schedules, cryptography (the study of secret codes), Internet security, and the safety of financial transactions. One branch of mathematics of particular importance to this study is group theory . Physicists and chemists rely on group theory to study the behavior of the tiniest particles that make up an atom in a scientific field known as quantum mechanics . Group theory also plays an important role in robotics, computer graphics, weather forecasting, musical theory, and medical image analysis. Matrices are essential to a branch of mathematics called linear algebra . Matrices and linear algebra are used in virtually all computer programs and electronic devices we use in our lives daily. b Mathematical systems have many applications in many scientific fields, including chemistry and physics. PhotoSky/123RF Mathematical Systems 9 Sections 9. 1 Groups 9. 2 Finite Mathematical Systems 9. 3 Modular Arithmetic 9. 4 Matrices
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