## Optional Advanced Mathematics Courses

The courses listed in this section are not required for admission but can provide useful background.

Subject | Rutgers Course | Course Abstract | Primary Textbook |
---|---|---|---|

Mathematical reasoning | Math 01:640:300 (3) Introduction to Mathematical Reasoning |
Fundamental abstract concepts common to all branches of mathematics. Special emphasis placed on ability to understand and construct rigorous proofs. | A Transition To Advanced Mathematics, by Smith, Eggen, St. Andre |

Advanced calculus I | Math 01:640:311 (4) Advanced Calculus I |
Introduction to language and fundamental concepts of analysis. The real numbers, sequences, limits, continuity, differentiation in one variable. | Introduction to Analysis by Edward D. Gaughan, 5th edition, Brooks/Cole, 1998 |

Advanced calculus II | Math 01:640:312 (2) Advanced Calculus II |
Continuation of Advanced Calculus I | Advanced Calculus by Patrick Fitzpatrick; Brooks/Cole, 2006 |

Introduction to numerical analysis II | Math 01:640:374 (3) Numerical Analysis II |
Continuation of Numerical Analysis I | Numerical Analysis by R.Burden & J.Faires; Brooks/Cole, 2005 |

Mathematical analysis I | Math 01:640:411 (3) Mathematical Analysis I |
Rigorous analysis of the differential and integral calculus of one and several variables. | Principles of Mathematical Analysis by Walter Rudin, 3rd edition, McGraw-Hill, 1976 |

Mathematical analysis II | Math 01:640:412 (3) Mathematical Analysis II |
Continuation of Mathematical Analysis I | Principles of Mathematical Analysis by Walter Rudin, 3rd edition, McGraw-Hill, 1976 |

Applied mathematics | Math 01:640:426 (3) Topics in Applied Mathematics |
Topics selected from integral transforms, calculus of variations, integral equations, Green's functions; applications to mathematical physics. |