Can You Prove God?

So I'm taking a class this semester called, "Religions of the West." It's about Christianity, Judaism, and Islam (and Atheism actually). Before I even walked in the classroom on the first day, I knew it was going to be a fascinating class. Oh, and let this be a warning, because it is a philosophy class and it's about religions-- it really makes me think--which will cause a lot of blogs! I am excited to learn about the different religions and process what I learned. I'm especially excited to see how it will strengthen my own beliefs and theology. So here goes the first digestion of topics discussed last week:

In my class, the first religion we are studying is atheism. It really helps to understand what people believe when they don't believe in a higher being. At first, I thought it was weird to be studying atheism in a religions class, but come to find out, a religion is just a set of beliefs. We could have gotten into the discussion about if capitalism could be considered a religion, but thankfully my teacher spared me that boredom (at least for now... who knows what the rest of the semester holds)! Anyway, we are studying prominent and influential atheists-- Marx, Freud, and some guy I can't remember the name of (give me a break, it's only been 2 weeks of class!). Last week we discussed Marx's ideas about religion. It was fascinating! Marx believed that the poor believed in the Bible, and especially the idea of Heaven, to give them hope and religion helped the rich keep them in their low positions. The rich got richer while they exploited the poor who believed they'd get something better someday. Marx saw this as weak. He believed people needed a reason for their suffering and "the last will become first" idea gave them that reason.
My thoughts on this is how can hanging on to hope be considered weak? Since when is hope weak? It is the source of life! It is what keeps people going from day to day, even when those days are bleak and gray. Jesus hung out with the poor and hopeless-- they are who he loved (he loves everyone, of course), but he especially came for the lowly people-- those who needed hope, the doctor to the sick.
Also, if there is no afterlife, what is the purpose of living? For what purpose do we do good works and love other people if our lives and souls end when our heart stops beating? If we have no one to tell us what makes life worth living, what is the purpose of living? Why wouldn't people just do what they want? (which gets into the debate of whether people are inherently good or evil...)
Another thought: Why do people submit our own lives to an incomprehensible being, someone we can't actually measure or evaluate or really even understand? Religion becomes a very personal experience. God is real to those who believe in him and experience him. God is everywhere. But how do you prove His existence? Is there any way to take the personal experience with God into public, outside of the walls of your bedroom and the walls of your church? Is it just shown through our actions and our love? I know God is real and alive and omnipresent, but how can I convey that to everyone else? I know showing his unconditional love is key to it all... but is there anything else? How we can show God to other people is a very personal experience and decision and walk for everyone. God works in so many ways-- there is no set mold or equation that God uses for everyone. That's what makes God amazing!
There are so many thoughts and questions and ideas running through my head, I can't even begin to type fast enough! I know I've only begun to scratch the surface of this theological discussion, so I would love to hear everyone else's thoughts!
What are everyone's thoughts? If you were to talk to Marx about his views on religion (this is not about his political ideas and/or communism), what would you ask him? I'd love to hear anyone and everyone's thoughts!!