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ABOUT THE COURSE: This course will cover the fundamental theory of Fourier series and Fourier integrals, as well as Fourier series for finite abelian groups. Some applications of Fourier series in differential equations, the isoperimetric problem, and number theory will be explored. Basic calculus and Riemann integrals will be required as prerequisites. The book “Introduction to Fourier Analysis” by E. Stein and R. Shakarchi will serve as the basis for this course.INTENDED AUDIENCE: UndergraduatePREREQUISITES: Basic Calculus, Riemann IntegrationINDUSTRY SUPPORT: This topic holds significant importance in mathematics and is considered a central theme that every mathematics student should be familiar with.