>>12454255PC - HTPI
BM - HTPI
BoP - BoP
BM - BoP
all fine at this point.
apostol v2 - Spivak
apostol v2 is patently retarded as you have not read v1 (v2 is multivariable and linear algebra) so Spivak is the only choice, and it's hard, but you are a math major so whatever.
PC - HTPI - Spivak
BM - HTPI - Spivak
BoP - BoP - Spivak
BM - BoP - Spivak
At this point you have zero experience with linear algebra
but again math major so whatever
PC - HTPI - Spivak - H&K
BM - HTPI - Spivak - H&K
BoP - BoP - Spivak - H&K
BM - BoP - Spivak - H&K
PC - HTPI - Spivak - LADR
BM - HTPI - Spivak - LADR
BoP - BoP - Spivak - LADR
BM - BoP - Spivak - LADR
All the algebra books are graduate level tomes (D&F 80% tome 20% graduate, C0 40% tome 50% graduate, Lang 100& graduate 100% tome) except for pinter which is woefully insufficient following spivak and especially H&K so remove H&K.
PC - HTPI - Spivak - LADR - Pinter
BM - HTPI - Spivak - LADR - Pinter
BoP - BoP - Spivak - LADR - Pinter
BM - BoP - Spivak - LADR - Pinter
rudin/tao is fine C&J is just apostol v1
PC - HTPI - Spivak - LADR - Pinter - Rudin
BM - HTPI - Spivak - LADR - Pinter - Rudin
BoP - BoP - Spivak - LADR - Pinter - Rudin
BM - BoP - Spivak - LADR - Pinter - Rudin
PC - HTPI - Spivak - LADR - Pinter - Tao
BM - HTPI - Spivak - LADR - Pinter - Tao
BoP - BoP - Spivak - LADR - Pinter - Tao
BM - BoP - Spivak - LADR - Pinter - Tao
From here the only books that are tenable are
Alphors
Munkres
Carmo
What a shit way to ruin your mathematical career.
I guess you could go D&F and Keep H&K
so the unnecessarily hard route would be
PC - HTPI - Spivak - H&K - D&F - Rudin
BM - HTPI - Spivak - H&K - D&F - Rudin
BoP - BoP - Spivak - H&K - D&F - Rudin
BM - BoP - Spivak - H&K - D&F - Rudin
PC - HTPI - Spivak - H&K - D&F - Tao
BM - HTPI - Spivak - H&K - D&F - Tao
BoP - BoP - Spivak - H&K - D&F - Tao
BM - BoP - Spivak - H&K - D&F - Tao