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.