\documentclass{amsart}
\usepackage{booktabs,longtable}
\usepackage[letterpaper, a4paper, total={7.5in, 10in}]{geometry}
\usepackage[table,usenames,dvipsnames]{xcolor}
\usepackage{makecell}
\begin{document}
\small
\rowcolors{2}{Gray!10}{white}
\begin{longtable}{@{}lllll@{}}
\toprule
Date & Lecture & \makecell[l]{Online Homework\\(MyLabMath 10pm)} &
\makecell[l]{Hand-graded Homework\\(Submit in class)} & \\
\midrule
\endhead
08/23, Mon & Sec 1.1 & & & \\
08/25, Wed & Sec 1.2 & & & \\
08/27, Fri & Sec 1.3 & & & \\
08/30, Mon & Sec 1.4 & HW01, HW02, HW03 & & \\
09/01, Wed & Sec 1.5 (part 1) & HW04 & HW02, HW03 & \\
09/03, Fri & Sec 1.5 (part 2) & HW05 & & \\
09/06, Mon & Labor Day & & & \\
09/08, Wed & Sec 1.6 (part 1) & HW06 & HW04, HW05, HW06, & \\
09/10, Fri & Sec 1.6 (part 2) & HW07 & & \\
09/13, Mon & Sec 2.1 & HW08 & & \\
09/15, Wed & Sec 2.2 & HW09 & HW08 & \\
09/17, Fri & Sec 2.3 & HW10 & & \\
09/20, Mon & Sec 2.4, 2.5 & HW11 & & \\
09/22, Wed & Sec 3.1 & HW12 & HW09, HW10, HW11 & \\
09/24, Fri & Sec 3.2 & HW13 & & \\
09/27, Mon & Sec 3.3 (part 1) & HW14 & & \\
09/29, Wed & Sec 3.3 (part 2) & HW15 & HW12, HW13, HW14 & \\
10/01, Fri & Sec 3.4 & HW16 & & \\
10/04, Mon & Review for Exam 1 & & & \\
10/05, Tue & \makecell[l]{Exam 1, 8:00-9:00 pm\\(Sec 1.1--1.6, 2.1--2.5, 3.1--3.3)} & & & \\
10/06, Wed & No class & & & \\
10/08, Fri & Exam 1 Discussion & & & \\
10/11, Mon & October Break & & & \\
10/13, Wed & Sec 3.5 (part 1) & HW17 & HW16, HW17 & \\
10/15, Fri & Sec 3.5 (part 2) & HW18 & & \\
10/18, Mon & Sec 3.6 (part 1) & HW19 & & \\
10/20, Wed & Sec 3.6 (part 2) & HW20 & HW18, HW19 & \\
10/22, Fri & Sec 4.1 (part 1) & HW21 & & \\
10/25, Mon & Sec 4.1 (part 2), 4.2 & HW22 & & \\
10/27, Wed & Sec 5.1 & HW23 & HW20 & \\
10/29, Fri & Sec 5.2 (part 1) & HW24 & & \\
11/01, Mon & Sec 5.2 (part 2) & HW25 & & \\
11/03, Wed & Sec 5.5 & HW26 & HW23, HW24, HW25 & \\
11/05, Fri & Sec 5.3 & HW27 & & \\
11/08, Mon & Review for Exam 2 & & & \\
11/09, Tue & \makecell[l]{Exam 2, 8:00-9:00 pm\\(Sec 3.4--3.6, 4.1--4.2, 5.1--5.5)} & & & \\
11/10, Wed & Sec 5.6 & HW28 & HW26, HW27, HW28 & \\
11/12, Fri & Exam 2 Discussion & & & \\
11/15, Mon & Sec 5.7 & HW29 & & \\
11/17, Wed & Sec 7.1 & HW30 & HW29 & \\
11/19, Fri & Sec 7.2 & HW31 & & \\
11/22, Mon & No class & & & \\
11/24, Wed & Thanksgiving & & & \\
11/26, Fri & Thanksgiving & & & \\
11/29, Mon & Sec 7.3 & HW32 & & \\
12/01, Wed & Sec 7.4 & HW33 & HW30, HW31, HW32 & \\
12/03, Fri & Sec 7.5 & HW34 & & \\
12/06, Mon & Sec 7.6 & HW35 & & \\
12/08, Wed & Review for Final & HW36 & HW33, HW34, HW35, HW36 & \\
12/10, Fri & Review for Final & & & \\
\bottomrule
\end{longtable}

\end{document}