Gary,
First, I will try to explain the part below of the formula.
CHOOSE(WEEKDAY(MAX(A$3:A3),2),2,,1,1,3))))
If the weekday of the previous day is 1 - Mon, 2 - Tue , 3 - Wed, 4 - Thu, 5 - Fri, then the CHOOSE function choose 2, , 1, 1 and 3 (the number of days to add to the previous day to get the present day). Note that for the Tue weekday I don't add nothing (I only have Mon, Wed, Thu and Fri in the column A).
Now, the formulas for the class meetings counted:
<b>Excel 2007</b><table cellpadding="2.5px" rules="all" style=";background-color: #FFFFFF;border: 1px solid;border-collapse: collapse; border-color: #A6AAB6"><colgroup><col width="25px" style="background-color: #E0E0F0" /><col /><col /><col /></colgroup><thead><tr style=" background-color: #E0E0F0;text-align: center;color: #161120"><th></th><th>A</th><th>B</th><th>C</th></tr></thead><tbody><tr ><td style="color: #161120;text-align: center;">1</td><td style="font-weight: bold;text-align: center;;"> Begin Date </td><td style="font-weight: bold;text-align: center;;"> End Date </td><td style="font-weight: bold;text-align: center;;">ClassMeetings</td></tr><tr ><td style="color: #161120;text-align: center;">2</td><td style="text-align: center;;">9/15/2011</td><td style="text-align: center;;">11/4/2011</td><td style="text-align: center;;">30</td></tr><tr ><td style="color: #161120;text-align: center;">3</td><td style="text-align: center;;"></td><td style="text-align: center;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">4</td><td style="text-align: right;;">9/15 Thu</td><td style=";">9/15 (Th)-1</td><td style=";">9/15 (Th)-1</td></tr><tr ><td style="color: #161120;text-align: center;">5</td><td style="text-align: right;;">9/16 Fri</td><td style=";">9/16 (F)-2</td><td style=";">9/16 (F)-1</td></tr><tr ><td style="color: #161120;text-align: center;">6</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">7</td><td style="text-align: right;;">9/19 Mon</td><td style=";">9/19 (M)-3</td><td style=";">9/19 (M)-1</td></tr><tr ><td style="color: #161120;text-align: center;">8</td><td style="text-align: right;;">9/21 Wed</td><td style=";">9/21 (W)-4</td><td style=";">9/21 (W)-1</td></tr><tr ><td style="color: #161120;text-align: center;">9</td><td style="text-align: right;;">9/22 Thu</td><td style=";">9/22 (Th)-5</td><td style=";">9/22 (Th)-2</td></tr><tr ><td style="color: #161120;text-align: center;">10</td><td style="text-align: right;;">9/23 Fri</td><td style=";">9/23 (F)-6</td><td style=";">9/23 (F)-2</td></tr><tr ><td style="color: #161120;text-align: center;">11</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">12</td><td style="text-align: right;;">9/26 Mon</td><td style=";">9/26 (M)-7</td><td style=";">9/26 (M)-2</td></tr><tr ><td style="color: #161120;text-align: center;">13</td><td style="text-align: right;;">9/28 Wed</td><td style=";">9/28 (W)-8</td><td style=";">9/28 (W)-2</td></tr><tr ><td style="color: #161120;text-align: center;">14</td><td style="text-align: right;;">9/29 Thu</td><td style=";">9/29 (Th)-9</td><td style=";">9/29 (Th)-3</td></tr><tr ><td style="color: #161120;text-align: center;">15</td><td style="text-align: right;;">9/30 Fri</td><td style=";">9/30 (F)-10</td><td style=";">9/30 (F)-3</td></tr><tr ><td style="color: #161120;text-align: center;">16</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">17</td><td style="text-align: right;;">10/3 Mon</td><td style=";">10/3 (M)-11</td><td style=";">10/3 (M)-3</td></tr><tr ><td style="color: #161120;text-align: center;">18</td><td style="text-align: right;;">10/5 Wed</td><td style=";">10/5 (W)-12</td><td style=";">10/5 (W)-3</td></tr><tr ><td style="color: #161120;text-align: center;">19</td><td style="text-align: right;;">10/6 Thu</td><td style=";">10/6 (Th)-13</td><td style=";">10/6 (Th)-4</td></tr><tr ><td style="color: #161120;text-align: center;">20</td><td style="text-align: right;;">10/7 Fri</td><td style=";">10/7 (F)-14</td><td style=";">10/7 (F)-4</td></tr><tr ><td style="color: #161120;text-align: center;">21</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">22</td><td style="text-align: right;;">10/10 Mon</td><td style=";">10/10 (M)-15</td><td style=";">10/10 (M)-4</td></tr><tr ><td style="color: #161120;text-align: center;">23</td><td style="text-align: right;;">10/12 Wed</td><td style=";">10/12 (W)-16</td><td style=";">10/12 (W)-4</td></tr><tr ><td style="color: #161120;text-align: center;">24</td><td style="text-align: right;;">10/13 Thu</td><td style=";">10/13 (Th)-17</td><td style=";">10/13 (Th)-5</td></tr><tr ><td style="color: #161120;text-align: center;">25</td><td style="text-align: right;;">10/14 Fri</td><td style=";">10/14 (F)-18</td><td style=";">10/14 (F)-5</td></tr><tr ><td style="color: #161120;text-align: center;">26</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">27</td><td style="text-align: right;;">10/17 Mon</td><td style=";">10/17 (M)-19</td><td style=";">10/17 (M)-5</td></tr><tr ><td style="color: #161120;text-align: center;">28</td><td style="text-align: right;;">10/19 Wed</td><td style=";">10/19 (W)-20</td><td style=";">10/19 (W)-5</td></tr><tr ><td style="color: #161120;text-align: center;">29</td><td style="text-align: right;;">10/20 Thu</td><td style=";">10/20 (Th)-21</td><td style=";">10/20 (Th)-6</td></tr><tr ><td style="color: #161120;text-align: center;">30</td><td style="text-align: right;;">10/21 Fri</td><td style=";">10/21 (F)-22</td><td style=";">10/21 (F)-6</td></tr><tr ><td style="color: #161120;text-align: center;">31</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">32</td><td style="text-align: right;;">10/24 Mon</td><td style=";">10/24 (M)-23</td><td style=";">10/24 (M)-6</td></tr><tr ><td style="color: #161120;text-align: center;">33</td><td style="text-align: right;;">10/26 Wed</td><td style=";">10/26 (W)-24</td><td style=";">10/26 (W)-6</td></tr><tr ><td style="color: #161120;text-align: center;">34</td><td style="text-align: right;;">10/27 Thu</td><td style=";">10/27 (Th)-25</td><td style=";">10/27 (Th)-7</td></tr><tr ><td style="color: #161120;text-align: center;">35</td><td style="text-align: right;;">10/28 Fri</td><td style=";">10/28 (F)-26</td><td style=";">10/28 (F)-7</td></tr><tr ><td style="color: #161120;text-align: center;">36</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">37</td><td style="text-align: right;;">10/31 Mon</td><td style=";">10/31 (M)-27</td><td style=";">10/31 (M)-7</td></tr><tr ><td style="color: #161120;text-align: center;">38</td><td style="text-align: right;;">11/2 Wed</td><td style=";">11/2 (W)-28</td><td style=";">11/2 (W)-7</td></tr><tr ><td style="color: #161120;text-align: center;">39</td><td style="text-align: right;;">11/3 Thu</td><td style=";">11/3 (Th)-29</td><td style=";">11/3 (Th)-8</td></tr><tr ><td style="color: #161120;text-align: center;">40</td><td style="text-align: right;;">11/4 Fri</td><td style=";">11/4 (F)-30</td><td style=";">11/4 (F)-8</td></tr><tr ><td style="color: #161120;text-align: center;">41</td><td style=";"></td><td style=";"></td><td style=";"></td></tr><tr ><td style="color: #161120;text-align: center;">42</td><td style=";"></td><td style=";"></td><td style=";"></td></tr></tbody></table><p style="width:3.6em;font-weight:bold;margin:0;padding:0.2em 0.6em 0.2em 0.5em;border: 1px solid #A6AAB6;border-top:none;text-align: center;background-color: #E0E0F0;color: #161120">Sheet4</p><br /><br /><table width="85%" cellpadding="2.5px" rules="all" style=";border: 2px solid black;border-collapse:collapse;padding: 0.4em;background-color: #FFFFFF" ><tr><td style="padding:6px" ><b>Worksheet Formulas</b><table cellpadding="2.5px" width="100%" rules="all" style="border: 1px solid;text-align:center;background-color: #FFFFFF;border-collapse: collapse; border-color: #A6AAB6"><thead><tr style=" background-color: #E0E0F0;color: #161120"><th width="10px">Cell</th><th style="text-align:left;padding-left:5px;">Formula</th></tr></thead><tbody><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">C2</th><td style="text-align:left">=COUNT(<font color="Blue">A:A</font>)-1</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">A4</th><td style="text-align:left">=IF(<font color="Blue">ROWS(<font color="Red">A$4:A4</font>)=1,A$2,IF(<font color="Red">MAX(<font color="Green">A$3:A3</font>)=B$2,"",IF(<font color="Green">WEEKDAY(<font color="Purple">MAX(<font color="Teal">A3</font>),2</font>)=5,"",MAX(<font color="Purple">A$3:A3</font>)+CHOOSE(<font color="Purple">WEEKDAY(<font color="Teal">MAX(<font color="#FF00FF">A$3:A3</font>),2</font>),2,,1,1,3</font>)</font>)</font>)</font>)</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">B4</th><td style="text-align:left">=IF(<font color="Blue">A4="","",TEXT(<font color="Red">A4,"m/d"</font>)&" ("&CHOOSE(<font color="Red">WEEKDAY(<font color="Green">A4,2</font>),"M",,"W","Th","F"</font>)&")-"&COUNT(<font color="Red">A$4:A4</font>)</font>)</td></tr></tbody></table></td></tr></table><br /><table width="85%" cellpadding="2.5px" rules="all" style=";border: 2px solid black;border-collapse:collapse;padding: 0.4em;background-color: #FFFFFF" ><tr><td style="padding:6px" ><b>Array Formulas</b><table cellpadding="2.5px" width="100%" rules="all" style="border: 1px solid;text-align:center;background-color: #FFFFFF;border-collapse: collapse; border-color: #A6AAB6"><thead><tr style=" background-color: #E0E0F0;color: #161120"><th width="10px">Cell</th><th style="text-align:left;padding-left:5px;">Formula</th></tr></thead><tbody><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">C4</th><td style="text-align:left">{=IF(<font color="Blue">A4="","",TEXT(<font color="Red">A4,"m/d"</font>)&" ("&CHOOSE(<font color="Red">WEEKDAY(<font color="Green">A4,2</font>),"M",,"W","Th","F"</font>)&")-"&1+SUM(<font color="Red">--IF(<font color="Green">ISNUMBER(<font color="Purple">A$3:A3</font>),WEEKDAY(<font color="Purple">A$3:A3,2</font>)=WEEKDAY(<font color="Purple">A4,2</font>)</font>)</font>)</font>)}</td></tr></tbody></table><b>Entered with Ctrl+Shift+Enter.</b> If entered correctly, Excel will surround with curly braces {}.
<b>Note: Do not try and enter the {} manually yourself</b></td></tr></table><br />
I hope this help you to understand.
Markmzz