A typical major program (with the standard major) looks something like this:

YEAR | FRESHMAN | SOPHOMORE | JUNIOR | SENIOR |

fall | 2250 | 2270 3200 |
3100 4700 |
4600/4500 4150 |

spring | 2260 | 3000 2700 | 4000 4720/4780 | 4400/4250 4750/4790 |

For students pursuing the area of emphasis in applied mathematics:

YEAR | FRESHMAN | SOPHOMORE | JUNIOR | SENIOR |

fall | 2250 | 2270 3200 |
3100 4500/4600 |
4500/4600 4700 |

spring | 2260 | 3300 2700 | 4510/4750/4720 | xxxx |

For students who have placed out of MATH 2250 (Calculus I)—for the standard major:

YEAR | FRESHMAN | SOPHOMORE | JUNIOR | SENIOR |

fall | 2260/2310H | 3000 2700 |
4000 4600/4700/4150 |
xxxx |

spring | 2270 3200/3100H |
3100 4690/4250 |
4010 4720/4780/4150 |
xxxx |

For students who have placed out of MATH 2250 (Calculus I)—for the applied area of emphasis:

YEAR | FRESHMAN | SOPHOMORE | JUNIOR | SENIOR |

fall | 2260 | 3300 2700 |
4500 4600 |
4700/xxxx |

spring | 2270 3200 |
3100 xxxx |
4510 xxxx |
4720/4780/xxxx |

A more aggressive choice might be this:

YEAR | FRESHMAN | SOPHOMORE | JUNIOR | SENIOR |

fall | 2260 | 3500(H) |
4000 4600/4700/4150 |
4100 xxxx |

spring | 3200/3100H 2700 |
3510(H) xxxx |
4010 4720/4780/4150 |
4200 xxxx |

For students who've scored a 5 on the BC Advanced Placement Calculus Exam and wish to start with multivariable calculus of some flavor:

YEAR | FRESHMAN | SOPHOMORE | JUNIOR | SENIOR |

fall | 3500(H) or 2270/2500 and 3200 |
4000 | 4100/4500 4670/4450 |
4220/8xxx 4700 |

spring | 3510(H) or 2700 and 3000 |
4010 3100(H) |
4200/4510 4250 |
xxxx xxxx |

You should consult with a mathematics advisor to figure out a suitable major program for you and discuss any questions you might have.