Intensive Chemotherapy and Rituximab in the Treatment of Burkitt Lymphoma

* Patients will be placed into one of two groups, "low risk" and "high risk". "Low risk" disease is defined as one area of disease measuring less than 10cm and a normal blood test called LDH (lactate hydrogenase). Patients not fitting the "low risk" criteria are considered "high risk". * If the patient has "low risk" disease their treatment cycle consist of three cycles of A. * If the patient has "high risk" disease they will receive Cycle A followed by cycle B which will then repeat. * Cycle A consists of the drugs: rituximab, cyclophosphamide, oncovin, doxorubicin and methotrexate (R-CODOX-M). The treatment cycle is approximately 14 days. A spinal tap is performed on day 1 and day 3 of the cycle and the patient will be hospitalized until between day 11 and day 13. After the patient's blood counts return to normal(usually around day 21),the next round of treatment will occur. * Cycle B consists of the drugs: rituximab, ifosfamide, VP-16 and ara-c (IVAC). The treatment cycle is approximately 5 days. A spinal tap is performed on day 4 and once blood counts return to normal the patient will start cycle A again. * After the patient has finished the treatments, they will be re-evaluated with CT scans and PET scans to determine whether or not they are in remission. Every three months for two years, blood tests and CT and PET scans will be performed. Follow up after that will be every 6 months for two years.