Most programming languages provide a way to get the week number of a given date. For an SQL example, check out my previous article: SQL: year of an ISO week.
In C# you can use the following:
int week = CultureInfo.CurrentCulture.Calendar.GetWeekOfYear(date, CalendarWeekRule.FirstFourDayWeek, DayOfWeek.Monday);
But there's usually no function provided to get the first day of a given week and year. The shortest (but still readable) way that I can get up with in C# is the following: